(1390,83,'Which of the following is the key highlight of the GST law?','','multi','single','','','1','1',NULL,'3','1','1','0','1','2021-05-27 13:06:25','2021-05-27 13:06:25'),(1391,83,'Mr A is a manufacturer. The tax payable on output (FINAL PRODUCT) is Rs 450. The tax paid on input (PURCHASES) is Rs 100. The tax paid on capital goods is Rs 200. What is the total ITC available in the above illustration?','','multi','single','','','1','1',NULL,'1','3','1','0','1','2021-05-27 13:19:44','2021-05-27 13:19:44'),(1392,83,'Mr A is a manufacturer. The tax payable on output (FINAL PRODUCT) is Rs 450. The tax paid on input (PURCHASES) is Rs 100. The tax paid on capital goods is Rs 200. What is the total Tax payable post ITC utilization in the above illustration?','','multi','single','','','1','1',NULL,'2','3','1','0','1','2021-05-27 13:35:21','2021-05-27 13:35:21'),(1393,83,'ITC can be claimed only for the:','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-05-27 13:37:40','2021-05-27 13:37:40'),(1394,83,'The details of reversal of ITC will be furnished in','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-05-27 13:44:18','2021-05-27 13:44:18'),(1395,83,'ITC on Transfer of Business can be transferred to the new business vide:','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-05-27 13:47:29','2021-05-27 13:47:29'),(1396,83,'If total ITC on inputs of exempted/non-business purpose is more than the ITC actually reversed during the year then the difference amount will be added to','','multi','single','','','1','5',NULL,'3','1','1','0','1','2021-05-27 13:59:52','2021-05-27 13:59:52'),(1397,83,'Which of the following documents is NOT required for claiming ITC?','','multi','single','','','1','7',NULL,'3','1','1','0','1','2021-05-27 14:06:03','2021-05-27 14:06:03'),(1398,83,'Which of the following person cannot claim ITC?','','multi','single','','','1','2',NULL,'2','1','1','0','1','2021-05-27 14:18:54','2021-05-27 14:18:54'),(1399,85,'1.1.1 Refer to the media for fill in the blank question.','','multi','html','<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">The time of supply fixes the point when the _____________&nbsp; to / of GST arises.</span></span></span></p>','','1','1.1.1',NULL,'1','1','1','0','1','2021-05-27 15:59:03','2021-05-27 15:59:03'),(1400,85,'What is time of supply of goods under CGST ?','','multi','single','','','1','1.3.1',NULL,'4','1','1','0','1','2021-05-27 16:07:10','2021-05-27 16:07:10'),(1401,85,'Date on which the supplier receives the payment as per section 12 of CGST Act is','','multi','single','','','1','1',NULL,'3','1','1','0','1','2021-05-27 16:12:16','2021-05-27 16:12:16'),(1402,85,'What is the time of supply of goods liable to tax under the reverse charge mechanism?','','multi','single','','','1','1.4.1',NULL,'4','1','1','0','1','2021-05-27 16:17:49','2021-05-27 16:17:49'),(1403,85,'What is the time of supply of service if the invoice is issued within 30 days from the date of provision of service?','','multi','single','','','1','1.3',NULL,'4','1','1','0','1','2021-05-27 17:34:06','2021-05-27 17:34:06'),(1404,85,'Refer to the media for the question.','','multi','html','<p><span style=\"font-size:14px\">Mr. X enters into a contract with a client for supply of certain services on 18.12.2017. GST is payable on such services under forward charge. Services are supplied on 25.12.2017 and invoiced on 05.01.2018. The client makes payment by cheque for the services on 29.12.2017 and such payment is credited to the bank account of Mr. X on 06.01.2018. The payment is recorded in the books of account of the client and Mr. X on 30.12.2017 and 07.01.2018 respectively. The time of supply of services is:</span></p>','','1','1.3',NULL,'4','1','1','0','1','2021-05-27 17:19:15','2021-05-27 22:49:14'),(1405,85,'What is the time of supply of goods under CGST ?','','multi','single','','','1','1.2',NULL,'4','1','1','0','1','2021-05-27 17:48:02','2021-05-27 17:48:02'),(1406,85,'What is the date of receipt of payment?','','multi','single','','','1','1',NULL,'3','1','1','0','1','2021-05-27 17:52:21','2021-05-27 17:52:21'),(1407,85,'What is the time of supply of service in case an associated enterprise receives services from the service provider located outside India?','','multi','single','','','1','1.6',NULL,'3','1','1','0','1','2021-05-27 17:56:28','2021-05-27 17:56:28'),(1408,85,'On 04.09.2018, supplier invoices goods taxable on reverse charge basis to ABC & Co. ABC & Co. receives the goods on 12.09.2018 and makes payment on 30.9.2018. determine the time of supply.','','multi','single','','','1','1.4',NULL,'3','3','1','0','1','2021-05-27 17:21:42','2021-05-27 22:51:42'),(1409,85,'What is the time of supply of goods, in case supplier opting for composition levy under section 10 of the CGST ACT, 2017?','','multi','single','','','1','1.2',NULL,'4','1','1','0','1','2021-05-27 18:09:47','2021-05-27 18:09:47'),(1410,88,'<p>1 Introduction of the Programme</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227009801622700980.mp4','','1','1','Introduction of the Programme','1','2','1','0','1','2021-06-03 11:46:21','2021-11-09 12:51:52'),(1411,88,'<p>2 Introduction of instructor</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227010521622701052.mp4','','1','2','Introduction of instructor','1','2','1','0','1','2021-06-28 06:31:08','2021-11-09 12:57:28'),(1412,88,'<p>3 Import license</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227011521622701152.mp4','','1','3','Import license','1','2','1','0','1','2021-06-03 11:49:12','2021-11-09 13:04:46'),(1413,88,'<p>4 Section 10(5) &amp; 10 (6) - FEMA</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227012631622701263.mp4','','1','4','Section 10(5) & 10 (6) - FEMA','1','2','1','0','1','2021-06-03 11:51:04','2021-11-09 13:08:21'),(1414,88,'<p>5 Electronic bank realization certificate</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227013311622701331.mp4','','1','5','Electronic bank realization certificate','1','2','1','0','1','2021-06-03 11:52:12','2021-11-09 13:09:19'),(1415,88,'<p>6 IEC No.</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227013971622701397.mp4','','1','6','IEC No.','1','2','1','0','1','2021-06-04 11:07:21','2021-11-09 13:10:44'),(1416,88,'<p>7 Some restrictions</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227014591622701459.mp4','','1','7','Some restrictions','1','2','1','0','1','2021-06-03 11:54:20','2021-11-09 13:11:32'),(1417,88,'<p>8 Passenger baggage</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227015181622701518.mp4','','1','8','Passenger baggage','1','2','1','0','1','2021-06-03 11:55:19','2021-11-09 13:11:57'),(1418,88,'<p>9 ITC - HS</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227015821622701582.mp4','','1','9','ITC - HS','1','2','1','0','1','2021-06-03 11:56:24','2021-11-09 13:12:26'),(1419,88,'<p>10 Import of foreign exchange/Indian rupees</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227016451622701645.mp4','','1','10','Import of foreign exchange/Indian rupees','1','2','1','0','1','2021-06-03 11:57:26','2021-11-09 13:12:59'),(1420,88,'<p>11 Third party payment for Import</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227016951622701695.mp4','','1','11','Third party payment for Import','1','2','1','0','1','2021-06-03 11:58:16','2021-11-09 13:13:34'),(1421,88,'<p>12 Advance remittance for Import of goods/services</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227017421622701742.mp4','','1','12','Advance remittance for Import of goods/services','1','2','1','0','1','2021-06-03 11:59:03','2021-11-09 13:14:12'),(1422,88,'<p>13 Interest on Import bills</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227017881622701788.mp4','','1','13','Interest on Import bills','1','2','1','0','1','2021-06-03 11:59:49','2021-11-09 13:14:47');
INSERT INTO `tbl_course_question` VALUES (1423,88,'<p>14 Receipt of Import documents by Importer directly</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227018401622701840.mp4','','1','14','Receipt of Import documents by Importer directly','1','2','1','0','1','2021-06-03 12:00:41','2021-11-09 13:15:17'),(1424,88,'<p>15 Evidence of Import</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227018991622701898.mp4','','1','15','Evidence of Import','1','2','1','0','1','2021-06-03 12:01:39','2021-11-09 13:15:47'),(1425,88,'<p>16 Types of bill of entry</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227019481622701948.mp4','','1','16','Types of bill of entry','1','2','1','0','1','2021-06-03 12:02:28','2021-11-09 13:16:09'),(1426,88,'<p>17 Non-physical Imports</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227019961622701996.mp4','','1','17','Non-physical Imports','1','2','1','0','1','2021-06-03 12:03:16','2021-11-09 13:16:38'),(1427,88,'<p>18 IDPMS</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227020451622702044.mp4','','1','18','IDPMS','1','2','1','0','1','2021-06-03 12:04:05','2021-11-09 13:22:46'),(1428,88,'<p>19 Extension &amp; write-off</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227020911622702091.mp4','','1','19','Extension & write-off','1','2','1','0','1','2021-06-03 12:04:52','2021-11-09 13:17:06'),(1429,88,'<p>20 Follow- up for evidence of Import</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227021361622702136.mp4','','1','20','Follow- up for evidence of Import','1','2','1','0','1','2021-06-03 12:05:36','2021-11-09 13:18:57'),(1430,88,'<p>21 Follow-up for Import evidence</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227021731622702173.mp4','','1','21','Follow-up for Import evidence','1','2','1','0','1','2021-06-03 12:06:13','2021-11-09 13:19:27'),(1431,88,'<p>22 Import of gold</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227022261622702226.mp4','','1','22','Import of gold','1','2','1','0','1','2021-06-03 12:07:07','2021-11-09 13:19:58'),(1432,88,'<p>24 Write-off of unrealized amount of Export leg</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227033161622703316.mp4','','1','24','Write-off of unrealized amount of Export leg','1','2','1','0','1','2021-06-03 12:25:17','2021-11-09 13:20:41'),(1433,88,'<p>25 Third party 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countries','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227096851622709685.mp4','','1','25',NULL,'1','2','1','0','1','2021-06-03 14:11:26','2021-06-03 14:11:26'),(1460,89,'26 Direct dispatch of documents by Exporter','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227097731622709773.mp4','','1','26',NULL,'1','2','1','0','1','2021-06-03 14:12:53','2021-06-03 14:12:53'),(1461,89,'27 Part drawings /undrawn balances','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227100751622710075.mp4','','1','27',NULL,'1','2','1','0','1','2021-06-03 14:17:55','2021-06-03 14:17:55'),(1462,89,'28  Consignment Exports','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227101321622710132.mp4','','1','28',NULL,'1','2','1','0','1','2021-06-03 14:18:53','2021-06-03 14:18:53'),(1463,89,'29 Extension of 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payables','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227107271622710727.mp4','','1','33',NULL,'1','2','1','0','1','2021-06-03 14:28:48','2021-06-03 14:28:48'),(1468,89,'34 Remittances connected with Export','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227107811622710781.mp4','','1','34',NULL,'1','2','1','0','1','2021-06-03 14:29:41','2021-06-03 14:29:41'),(1469,89,'35 Refund of Export proceeds','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227108361622710836.mp4','','1','35',NULL,'1','2','1','0','1','2021-06-03 14:30:37','2021-06-03 14:30:37'),(1470,88,'Which of the following section of Foreign Exchange Management Act 1999 (42 of 1999) ,','','multi','single','','','1','1',NULL,'1','1','1','1','1','2021-08-07 04:19:07','2021-08-07 09:49:07'),(1471,88,'Foreign Exchange Management (Current Account Transaction) Rules, 2000. - Notification on which of the following date','','multi','single','','','1','1',NULL,'1','1','1','1','1','2021-08-07 04:22:46','2021-08-07 09:52:46'),(1472,88,'RBI directions to AP under which of the  following Section  of Foreign Exchange Management Act (FEMA), 1999','','multi','single','','','1','1',NULL,'4','2','1','1','1','2021-08-07 04:18:54','2021-08-07 09:48:54'),(1473,88,'Research & Development Cess Act, 1986 for import of which of the following','','multi','single','','','1','1',NULL,'3','1','1','1','1','2021-08-07 04:22:21','2021-08-07 09:52:21'),(1474,88,'Import trade regulated by which of the following','','multi','single','','','1','1',NULL,'1','1','1','1','1','2021-08-07 04:23:16','2021-08-07 09:53:16'),(1475,88,'AD to preserve utilised licence till verified by','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-03 15:57:44','2021-06-03 21:27:44'),(1476,88,'Person acquiring foreign exchange may use it for','','multi','single','','','1','4',NULL,'2','1','1','0','1','2021-06-03 15:59:36','2021-06-03 21:29:36'),(1477,88,'Importer furnishes evidence of import for which of the following','','multi','single','','','1','4',NULL,'1','1','1','0','1','2021-06-03 16:00:00','2021-06-03 21:30:00'),(1478,88,'DGFT captures details of realisation of export proceeds directly  from which of the following','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-03 16:02:11','2021-06-03 21:32:11'),(1479,88,'MOU signed with which government','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-03 16:02:28','2021-06-03 21:32:28'),(1480,88,'Sharing of EBRC data to facilitate refund of  which of the following','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-03 16:05:58','2021-06-03 21:35:58'),(1481,88,'IEC is allotted to','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-03 16:11:12','2021-06-03 21:41:12'),(1482,88,'IEC No is  Mandatory for undertaking which of the following','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-04 11:08:17','2021-06-04 16:38:17'),(1483,88,'Permanent validity unless cancelled by  which of the following','','multi','single','','','1','6',NULL,'4','1','1','0','1','2021-06-03 16:12:24','2021-06-03 21:42:23'),(1484,88,'IEC will cover all','','multi','single','','','1','6',NULL,'4','1','1','0','1','2021-06-03 16:12:46','2021-06-03 21:42:46'),(1485,88,'Upload documents & pay fee through','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-03 16:13:32','2021-06-03 21:43:32'),(1486,88,'DGFT may, impose restrictions on which of the following','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-03 16:13:58','2021-06-03 21:43:58'),(1487,88,'Restricted Goods may be exported in accordance with Authorisation prescribed in','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-04 11:08:57','2021-06-04 16:38:57'),(1488,88,'Goods importable freely without any ‘Restriction’ may be imported by','','multi','single','','','1','6',NULL,'4','1','1','0','1','2021-06-03 16:15:02','2021-06-03 21:45:02'),(1489,88,'Samples of tea not exceeding (CIF)','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-03 16:18:27','2021-06-03 21:48:27'),(1490,88,'Duty free Import of samples up to Rs.3,00,000 for all','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-03 16:18:49','2021-06-03 21:48:49'),(1491,88,'No Authorisation required for Import of','','multi','single','','','1','7',NULL,'3','1','1','0','1','2021-06-03 16:19:28','2021-06-03 21:49:28'),(1492,88,'Items restricted in ITC (HS) except','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-03 16:19:55','2021-06-03 21:49:55'),(1493,88,'Application for CCP for import of restricted for Imports in ITC (HS) as gifts to the','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-03 16:20:22','2021-06-03 21:50:22'),(1494,88,'Payment of Customs duty, shall be allowed by Customs authorities without which of the following','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-03 16:20:57','2021-06-03 21:50:57'),(1495,88,'Recipient of a gift is','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-03 16:21:34','2021-06-03 21:51:34'),(1496,88,'Limits, terms & conditions notified by','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-03 16:22:46','2021-06-03 21:52:46'),(1497,88,'Samples of otherwise freely importable may be imported as passenger baggage without which of the following','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-03 16:23:08','2021-06-03 21:53:08'),(1498,88,'Exporters coming from abroad allowed to Import','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-03 16:23:30','2021-06-03 21:53:30'),(1499,88,'Prohibition’, ‘restriction’ / ‘exclusive trading through','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-03 16:26:36','2021-06-03 21:56:36'),(1500,88,'Compilation of codes for merchandise / goods for','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-03 16:27:01','2021-06-03 21:57:01'),(1501,88,'Goods classified based on their group or sub-group at which digit','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-03 16:27:36','2021-06-03 21:57:36'),(1502,88,'India maintains national Harmonized System of goods at which digit level','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-03 16:28:10','2021-06-03 21:58:10'),(1503,88,'Under which of the following policies for all goods are indicated against each item in ITC (HS)','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-03 16:28:43','2021-06-03 21:58:43'),(1504,88,'Schedule 2 of ITC (HS) details which  Policy regime','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-03 16:29:12','2021-06-03 21:59:12'),(1505,88,'Schedule 1 of ITC (HS) lays down which Policy regime.','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-03 16:30:18','2021-06-03 22:00:18'),(1506,88,'Where it is clearly specified, Import Policy is for new goods','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-03 16:30:47','2021-06-03 22:00:47'),(1507,88,'Payment for Import can be made through which of the following','','multi','single','','','1','9',NULL,'4','1','1','0','1','2021-06-03 16:31:13','2021-06-03 22:01:13'),(1508,88,'Whom special permission is required, Import or bring into India, any foreign currency.','','multi','single','','','1','10',NULL,'4','1','1','0','1','2021-06-03 16:32:34','2021-06-03 22:02:34'),(1509,88,'A person Send into India, without limit, foreign exchange in any form other than','','multi','single','','','1','10',NULL,'4','1','1','0','1','2021-06-03 16:33:15','2021-06-03 22:03:15'),(1510,88,'No need of declaration if currency notes, bank notes or travellers cheques does not exceed USD','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-03 16:33:38','2021-06-03 22:03:38'),(1511,88,'Aggregate value of currency notes does not exceed USD','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-03 16:34:07','2021-06-03 22:04:07'),(1512,88,'From Nepal or Bhutan, currency notes of India for any amount in denominations up to Rs','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-03 16:34:33','2021-06-03 22:04:33'),(1513,88,'Documentary evidence where name of the third party mentioned in irrevocable order / invoice','','multi','single','','','1','11',NULL,'3','1','1','0','1','2021-06-03 19:28:41','2021-06-03 19:28:41'),(1514,88,'Who satisfied with bonafides of transactions & consider Financial Action Task Force (FATF) Statement;','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-03 19:30:10','2021-06-03 19:30:10'),(1515,88,'Invoice to contain narration that related payment to be made to (named)','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-03 19:31:26','2021-06-03 19:31:26'),(1516,88,'Bill of Entry to mention name of','','multi','single','','','1','11',NULL,'4','1','1','0','1','2021-06-03 19:33:50','2021-06-03 19:33:50'),(1517,88,'Advance Remittance for Import of Rough','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-03 19:37:02','2021-06-03 19:37:02'),(1518,88,'Physical import within','','multi','single','','','1','12',NULL,'3','1','1','0','1','2021-06-03 19:41:57','2021-06-03 19:41:57'),(1519,88,'In case of deviation prior approval of','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-03 19:43:11','2021-06-03 19:43:11'),(1520,88,'Overdue interest on delayed payments for less than','','multi','single','','','1','13',NULL,'1','1','1','0','1','2021-06-03 19:45:40','2021-06-03 19:45:40'),(1521,88,'Import of Equipment by  which of the following for their Overseas Site','','multi','single','','','1','13',NULL,'1','1','1','0','1','2021-06-03 19:46:37','2021-06-03 19:46:37'),(1522,88,'What to be received from banker of supplier by banker of importer in India.','','multi','single','','','1','14',NULL,'1','1','1','0','1','2021-06-03 19:55:29','2021-06-03 19:55:29'),(1523,88,'AD not to make remittances where bills been received directly by','','multi','single','','','1','14',NULL,'1','1','1','0','1','2021-06-03 19:59:10','2021-06-03 19:59:10'),(1524,88,'Bills received by Status Holder Exporters, where Export Oriented Units','','multi','single','','','1','14',NULL,'1','1','1','0','1','2021-06-03 20:00:16','2021-06-03 20:00:16'),(1525,88,'What is received by public limited, deemed public limited & private limited companies?','','multi','single','','','1','14',NULL,'4','1','1','0','1','2021-06-03 20:01:46','2021-06-03 20:01:46'),(1526,88,'Semi-precious stones has received documents directly from overseas supplier & documentary evidence submitted - up to','','multi','single','','','1','14',NULL,'1','1','1','0','1','2021-06-03 20:02:57','2021-06-03 20:02:57'),(1527,88,'AD to fully satisfy about financial standing/status & track record of','','multi','single','','','1','14',NULL,'1','1','1','0','1','2021-06-03 20:04:40','2021-06-03 20:04:40'),(1528,88,'Which report need not be obtained where invoice value does not exceed USD 300,000?','','multi','single','','','1','14',NULL,'1','1','1','0','1','2021-06-03 20:09:19','2021-06-03 20:09:19'),(1529,88,'BoE number, port code and date for marking evidence of Import under','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-03 16:36:50','2021-06-03 22:06:50'),(1530,88,'who submits Customs Assessment Certificate / Postal Appraisal Form, /Courier Bill of Entry','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-03 16:37:19','2021-06-03 22:07:19'),(1531,88,'Who may allow if, If Importers fail to produce evidence due to genuine reasons','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-03 16:37:46','2021-06-03 22:07:46'),(1532,88,'Who  accept, in lieu of Exchange Control Copy of Bill of Entry for home consumption, a certificate from Chief Executive Officer bodies that goods for which remittance was made have actually been imported into India subject to conditions.','','multi','single','','','1','15',NULL,'3','1','1','0','1','2021-06-03 16:38:16','2021-06-03 22:08:16'),(1533,88,'Bills of entry are of how many types','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-03 16:39:08','2021-06-03 22:09:08'),(1534,88,'Ex-Bond Clearance is a type of','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-03 16:39:30','2021-06-03 22:09:30'),(1535,88,'If goods not required immediately, Importer may store in','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-03 16:39:54','2021-06-03 22:09:54'),(1536,88,'Goods classified & value assessed at the time of clearance from which of the following','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-03 16:40:26','2021-06-03 22:10:26'),(1537,88,'How many digit, BIN ( Business Identification Number) is allotted to each Importer','','multi','single','','','1','16',NULL,'2','1','1','0','1','2021-06-03 16:40:51','2021-06-03 22:10:51'),(1538,88,'Software or data through internet / datacom channel/ design has been received by which of the following','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-03 16:41:57','2021-06-03 22:11:57'),(1539,88,'AD shall enter BoE details (BoE number, port code and date) for which  associated','','multi','single','','','1','18',NULL,'4','1','1','0','1','2021-06-03 16:53:48','2021-06-03 22:23:48'),(1540,88,'Who shall generate ORM for Import payments made “BOE settlement','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-03 16:54:14','2021-06-03 22:24:14'),(1541,88,'Multiple ORMs can be settled against single BoE & multiple BoE can be settled against one','','multi','single','','','1','18',NULL,'2','1','1','0','1','2021-06-03 16:54:41','2021-06-03 22:24:41'),(1542,88,'On settlement of ORM with evidence of import AD shall issue','','multi','single','','','1','18',NULL,'3','1','1','0','1','2021-06-03 16:55:33','2021-06-03 22:25:33'),(1543,88,'AD shall give extension for submission of which of the following','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-03 16:56:58','2021-06-03 22:26:58'),(1544,88,'AD may consider closure of BoE/ORM in which of the following','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-03 16:57:22','2021-06-03 22:27:22'),(1545,88,'AD may close BoE transactions where write off is on account of which of the following','','multi','single','','','1','19',NULL,'4','1','1','0','1','2021-06-03 16:57:46','2021-06-03 22:27:46'),(1546,88,'AD to settle & close ORM/BoE with appropriate “Adjustment Indicator” in which of the following','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-03 16:58:18','2021-06-03 22:28:18'),(1547,88,'Internal inspectors / auditors of AD to carry out random sample check / percentage check of write-off of which of the following','','multi','single','','','1','19',NULL,'2','1','1','0','1','2021-06-03 16:58:41','2021-06-03 22:28:41'),(1548,88,'AD shall continue to follow up for outward remittance made for which of the following','','multi','single','','','1','20',NULL,'1','1','1','0','1','2021-06-03 17:00:24','2021-06-03 22:30:24'),(1549,88,'Relevant evidence of import data is not available in IDPMS on due dates against the ORM, AD shall follow up with which of the following','','multi','single','','','1','20',NULL,'1','1','1','0','1','2021-06-03 17:00:59','2021-06-03 22:30:59'),(1550,88,'AD should rigorously follow-up where at-least one communication by which of the following mode','','multi','single','','','1','21',NULL,'1','1','1','0','1','2021-06-03 17:02:44','2021-06-03 22:32:44'),(1551,88,'In which of the following all outstanding import remittances, irrespective of the amount involved, should be reported by AD','','multi','single','','','1','21',NULL,'1','1','1','0','1','2021-06-03 17:04:07','2021-06-03 22:34:07'),(1552,88,'Nominated banks & agencies, by DGFT, permitted to Import gold on which of the following  basis.','','multi','single','','','1','22',NULL,'1','1','1','0','1','2021-06-03 18:17:06','2021-06-03 23:47:06'),(1553,88,'Nominated banks are free to grant which of the following  loans','','multi','single','','','1','22',NULL,'2','1','1','0','1','2021-06-03 18:17:39','2021-06-03 23:47:39'),(1554,88,'Status Holder Exporters to adhere guidelines in','','multi','single','','','1','22',NULL,'1','1','1','0','1','2021-06-03 18:18:22','2021-06-03 23:48:22'),(1555,88,'Suppliers’ & Buyers’ credit should not exceed how many days from date of shipment.','','multi','single','','','1','22',NULL,'1','1','1','0','1','2021-06-03 18:19:38','2021-06-03 23:49:38'),(1556,88,'AD may allow extension of time in respect of such clean credit to a maximum period of how many days','','multi','single','','','1','22',NULL,'2','1','1','0','1','2021-06-05 04:03:10','2021-06-05 09:33:10'),(1557,88,'AD may handle which of the following','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-03 18:23:55','2021-06-03 23:53:55'),(1558,88,'Who permitted for Exports / Imports under Foreign Trade Policy (FTP) of India','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-03 18:28:14','2021-06-03 23:58:14'),(1559,88,'AD to satisfy with which of the following transactions','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-03 18:28:49','2021-06-03 23:58:49'),(1560,88,'Entire trade is to be routed through which of the following','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-03 18:29:19','2021-06-03 23:59:19'),(1561,88,'Who shall ensure that requisite details are made available /retrievable at the time of Inspection/ Audit / investigation of the transactions.','','multi','single','','','1','23',NULL,'2','1','1','0','1','2021-06-03 18:29:59','2021-06-03 23:59:59'),(1562,88,'Payment for Import leg may be allowed out of which of the following','','multi','single','','','1','23',NULL,'2','1','1','0','1','2021-06-03 18:30:48','2021-06-04 00:00:48'),(1563,88,'Advance payment for import leg beyond which of the following per transaction','','multi','single','','','1','23',NULL,'2','1','1','0','1','2021-06-03 18:32:01','2021-06-04 00:02:01'),(1564,88,'Prudential limits for advance payments may be fixed by which bank','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-03 18:32:35','2021-06-04 00:02:35'),(1565,88,'Merchant traders with outstanding  of how much their annual Export earnings shall be liable for caution listing?','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-03 18:35:10','2021-06-04 00:05:10'),(1566,88,'Who shall satisfy about capabilities of merchanting trader to perform obligations','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-03 18:35:54','2021-06-04 00:05:54'),(1567,88,'Who may write-off unrealized amount of Export leg, without any ceiling, on request of trader?','','multi','single','','','1','24',NULL,'2','1','1','0','1','2021-06-03 18:37:46','2021-06-04 00:07:46'),(1568,88,'Counterparty not from a country / jurisdiction in the updated FATF Public Statement on High Risk & Non-Co-operative Jurisdictions on which of the following has called for counter measures?','','multi','single','','','1','24',NULL,'1','1','1','0','1','2021-06-03 18:39:37','2021-06-04 00:09:37'),(1569,88,'Which party payments for Export & Import legs of MTT is not allowed?','','multi','single','','','1','25',NULL,'1','1','1','0','1','2021-06-03 18:41:33','2021-06-04 00:11:33'),(1570,88,'Agency commission not allowed in MTTs','','multi','single','','','1','25',NULL,'1','1','1','0','1','2021-06-03 18:43:34','2021-06-04 00:13:34'),(1571,88,'Who may allow agency commission up to a reasonable extent by outward remittance under exceptional circumstances?','','multi','single','','','1','25',NULL,'1','1','1','0','1','2021-06-03 18:44:33','2021-06-04 00:14:33'),(1572,88,'Who may approach Regional Office of RBI for regularization of the MTT for deviation?','','multi','single','','','1','25',NULL,'1','1','1','0','1','2021-06-03 18:45:08','2021-06-04 00:15:08'),(1573,88,'Which of the following are landlocked countries?','','multi','single','','','1','26',NULL,'3','1','1','0','1','2021-06-03 18:47:07','2021-06-04 00:17:07'),(1574,88,'Which of the following will handle all transactions through ACU?','','multi','single','','','1','27',NULL,'1','1','1','0','1','2021-06-03 18:49:58','2021-06-04 00:19:58'),(1575,88,'Who may  freely enter into correspondent arrangements with banks in other countries participating in Clearing Union?','','multi','single','','','1','27',NULL,'1','1','1','0','1','2021-06-03 18:50:54','2021-06-04 00:20:54'),(1576,88,'Terms ACU Dollar, ACU Euro & ACU Yen are used to identify use of which of  the following?','','multi','single','','','1','27',NULL,'4','1','1','0','1','2021-06-03 18:52:19','2021-06-04 00:22:19'),(1577,88,'For current international transactions as defined by Articles of Agreement of  which of the following','','multi','single','','','1','27',NULL,'1','1','1','0','1','2021-06-03 19:05:49','2021-06-04 00:35:49'),(1578,88,'Trade transactions with which country may be settled in any freely convertible currency, in addition to the ACU mechanism?','','multi','single','','','1','27',NULL,'2','1','1','0','1','2021-06-03 19:06:49','2021-06-04 00:36:49'),(1579,89,'On Which date FEMA 14 was notified?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-04 05:35:29','2021-06-04 11:05:29'),(1580,89,'EDF to be released only on receipt of funds in','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-04 05:10:14','2021-06-04 10:40:14'),(1581,89,'ACU transaction shall be equivalent in value to  which of the following?','','multi','single','','','1','4',NULL,'1','1','1','0','1','2021-06-04 04:44:47','2021-06-04 10:14:47'),(1582,89,'Transactions with which of the following can be settled in any freely convertible currency in addition to ACU.','','multi','single','','','1','4',NULL,'1','1','1','0','1','2021-06-04 05:46:28','2021-06-04 11:16:28'),(1583,89,'Which transactions with Iran to be settled in any permitted currency outside the ACU mechanism.','','multi','single','','','1','4',NULL,'4','1','1','0','1','2021-06-04 06:58:11','2021-06-04 12:28:11'),(1584,89,'AD to consider which statements?','','multi','single','','','1','5',NULL,'3','1','1','0','1','2021-06-04 04:54:40','2021-06-04 10:24:40'),(1585,89,'Firm irrevocable order backed by  which agreement ?','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-04 05:19:40','2021-06-04 10:49:40'),(1586,89,'Name of Which  party being mentioned in the irrevocable order/ invoice?','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-04 05:34:09','2021-06-04 11:04:09'),(1587,89,'Which one of the following is satisfied with the bona-fides of transaction & export documents','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-04 06:55:49','2021-06-04 12:25:49'),(1588,89,'Payment routed through which channel ?','','multi','single','','','1','5',NULL,'4','1','1','0','1','2021-06-04 05:36:27','2021-06-04 11:06:27'),(1589,89,'In case of imports, payment to be made to which party?','','multi','single','','','1','5',NULL,'3','1','1','0','1','2021-06-04 05:28:41','2021-06-04 10:58:41'),(1590,89,'Invoice contain narration that is related to which of the following','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-04 05:30:43','2021-06-04 11:00:43'),(1591,89,'Settlement of which transactions does not have a direct exchange rate.','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-04 05:42:26','2021-06-04 11:12:26'),(1592,89,'Which of the following  invoice in freely convertible currency?','','multi','single','','','1','6',NULL,'4','1','1','0','1','2021-06-04 06:53:49','2021-06-04 12:23:49'),(1593,89,'AD satisfied with the which of the following','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-04 04:52:45','2021-06-04 10:22:45'),(1594,89,'Participants in which of the following  open  foreign currency account','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-04 05:35:59','2021-06-04 11:05:59'),(1595,89,'Within how much time from closure of the exhibition/trade fair & details submitted to AD','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-04 07:08:14','2021-06-04 12:38:14'),(1596,89,'RBI may consider (Form EFC) opening foreign currency account with AD','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-04 05:38:35','2021-06-04 11:08:35'),(1597,89,'An Indian entity can open, hold & maintain foreign currency account on which of the following place','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-04 04:58:15','2021-06-04 10:28:15'),(1598,89,'Unit in a Special Economic Zone (SEZ) may open, hold and maintain a Foreign Currency Account with AD which of the following','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-04 05:47:53','2021-06-04 11:17:53'),(1599,89,'Firms & companies with a track record of at least 2 years in which of the following','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-04 05:22:09','2021-06-04 10:52:09'),(1600,89,'Firms & companies to have not more than ………………….DD accounts','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-04 12:03:40','2021-06-04 17:33:40'),(1601,89,'Resident in India may open which of the following account?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-04 05:40:43','2021-06-04 11:10:43'),(1602,89,'Facility not intended to  maintain assets in foreign currency, as India is still not fully convertible on which of the following account ?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-04 05:18:56','2021-06-04 10:48:56'),(1603,89,'Which of the following extend trade related loans/ advances to overseas importers.','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-04 05:52:20','2021-06-04 11:22:20'),(1604,89,'How much Payments received in foreign exchange by a Export Oriented Unit?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-04 05:27:54','2021-06-04 10:57:54'),(1605,89,'In Eligible Credits inward remittance through which banking?','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-04 05:29:41','2021-06-04 10:59:41'),(1606,89,'Counter trade proposals involving adjustment of value of goods imported into India against value of goods exported from India will be considered by which of the following','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-04 05:04:32','2021-06-04 10:34:32'),(1607,89,'Exports to neighbouring countries by which of the following','','multi','single','','','1','11',NULL,'4','1','1','0','1','2021-06-04 05:18:24','2021-06-04 10:48:24'),(1608,89,'Counter –Trade arrangements with','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-04 05:05:24','2021-06-04 10:35:24'),(1609,89,'Border trade with','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-04 05:02:10','2021-06-04 10:32:10'),(1610,89,'Remittance of commitment fee / service charges, etc., payable by exporter as approved by which of the following','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-04 05:40:14','2021-06-04 11:10:14'),(1611,89,'Which of the following permitted to factor Export receivables on a non-recourse basis,','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-04 06:55:14','2021-06-04 12:25:14'),(1612,89,'Which of the following have to obtain approval of AD / Exim Bank at post-award stage before undertaking execution of contracts','','multi','single','','','1','13',NULL,'2','1','1','0','1','2021-06-04 05:52:52','2021-06-04 11:22:52'),(1613,89,'Which of the following have to obtain approval of AD / Exim Bank at post-award stage before undertaking execution of contracts','','multi','single','','','1','14',NULL,'2','1','1','0','1','2021-06-04 06:52:50','2021-06-04 12:22:50'),(1614,89,'Inter-Project transfer which of the following','','multi','single','','','1','14',NULL,'3','1','1','0','1','2021-06-04 05:30:12','2021-06-04 11:00:12'),(1615,89,'Prior approval of RBI required in which of the following','','multi','single','','','1','14',NULL,'4','1','1','0','1','2021-06-04 05:36:51','2021-06-04 11:06:51'),(1616,89,'How many copies of Customs shall certify value & give running serial number on EDF.','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-04 05:25:19','2021-06-04 10:55:19'),(1617,89,'Customs shall retain original EDF for transmission to RBI & return duplicate to which of the following ?','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-04 05:07:02','2021-06-04 10:37:02'),(1618,89,'Exporters shall submit duplicate EDF to which of the following','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 05:15:17','2021-06-04 10:45:17'),(1619,89,'After examining goods, Customs shall certify quantity & return to exporter for submission to which of the following','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 04:57:37','2021-06-04 10:27:37'),(1620,89,'Within how many days, exporter shall lodge the duplicate copy together with shipping documents to AD.','','multi','single','','','1','15',NULL,'4','1','1','0','1','2021-06-04 07:07:43','2021-06-04 12:37:43'),(1621,89,'AD shall report transaction through Export Data Processing and Monitoring System (EDPMS) to which of the following','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 04:54:05','2021-06-04 10:24:05'),(1622,89,'Export of goods/ software done through','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 05:17:54','2021-06-04 10:47:54'),(1623,89,'Duplicate EDF shall be retained by which of the following','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 05:08:02','2021-06-04 10:38:02'),(1624,89,'Which Postal Authorities shall allow export of goods by post ?','','multi','single','','','1','15',NULL,'3','1','1','0','1','2021-06-04 06:56:25','2021-06-04 12:26:24'),(1625,89,'Who may, countersign EDF covering parcels addressed direct to the consignees','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 07:01:00','2021-06-04 12:31:00'),(1626,89,'Who can  file single / bulk SOFTEX form to competent authority for certification','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 06:59:10','2021-06-04 12:29:10'),(1627,89,'SOFTEX data from STPI/SEZ are transmitted in electronic format to which of the following','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-04 05:44:00','2021-06-04 11:14:00'),(1628,89,'Exporters have to submit SOFTEX in which form','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 05:14:46','2021-06-04 10:44:46'),(1629,89,'After certification STPI/SEZ will retain one copy & handover duplicate to which of the following','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-04 04:56:56','2021-06-04 10:26:56'),(1630,89,'Which of the following  have to provide information about all the invoices','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-04 06:53:26','2021-06-04 12:23:26'),(1631,89,'Last invoice / bill should be raised not later than how many days from date of completion of the contract.','','multi','single','','','1','15',NULL,'3','1','1','0','1','2021-06-05 04:02:50','2021-06-05 09:32:50'),(1632,89,'Who may consider requests for grant of EDF waiver from exporters','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-04 07:02:56','2021-06-04 12:32:56'),(1633,89,'Grant of EDF waiver on annual  limit of','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-05 04:00:55','2021-06-05 09:30:55'),(1634,89,'What is the annual limit For export of pharma products by pharmaceutical companies.','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-04 05:48:28','2021-06-04 11:18:28'),(1635,89,'supplies of pharmaceutical products annual limits up to','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-04 05:44:28','2021-06-04 11:14:28'),(1636,89,'Grant of which waiver Shall not be entitled to Duty Drawback or any other export incentive','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-04 05:25:52','2021-06-04 10:55:52'),(1637,89,'Advance payment (with or without interest), from a buyer is made with which of the following','','multi','single','','','1','16',NULL,'2','1','1','0','1','2021-06-05 04:08:16','2021-06-05 09:38:16'),(1638,89,'Shipment made within which of the following','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-04 05:42:56','2021-06-04 11:12:56'),(1639,89,'Rate of interest, if any, does not exceed which of the following','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-04 05:38:02','2021-06-04 11:08:02'),(1640,89,'No remittance towards refund of advance payment or interest, after expiry of which of the following','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-04 05:34:58','2021-06-04 11:04:58'),(1641,89,'Whose approval is required remittance towards refund of advance payment','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-04 07:05:44','2021-06-04 12:35:44'),(1642,89,'Prudential requirements based on which of the following approved policy.','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-04 05:37:30','2021-06-04 11:07:30'),(1643,89,'BG / SBLC issued from which of the following','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-04 05:01:16','2021-06-04 10:31:16'),(1644,89,'Refunding advance payment credited to which account','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-04 05:39:48','2021-06-04 11:09:48'),(1645,89,'AD may allow exporters to receive advance payment for export of goods which would take how Many years','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-04 04:47:19','2021-06-04 10:17:19'),(1646,89,'Which agreement provide for shipment of goods extending beyond period of one year','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-04 05:50:13','2021-06-04 11:20:13'),(1647,89,'Companies & organizations participating in Trade Fair can export goods for exhibition & sale outside India without prior approval which of the following','','multi','single','','','1','19',NULL,'2','1','1','0','1','2021-06-04 05:03:48','2021-06-04 10:33:48'),(1648,89,'What may sold outside exhibition/trade fair in same country.','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-05 04:10:32','2021-06-05 09:40:32'),(1649,89,'Sales at discounted value are','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-04 05:41:19','2021-06-04 11:11:19'),(1650,89,'Is it permissible to \'gift’ unsold goods up to USD 5000 per exporter, per exhibition.','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-04 05:31:19','2021-06-04 11:01:19'),(1651,89,'Who shall produce relative Bill of Entry within one month of re-import into India of unsold items.','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-04 07:06:09','2021-06-04 12:36:09'),(1652,89,'Who will report to AD method of disposal of all items exported, as well as repatriation of proceeds to India.','','multi','single','','','1','19',NULL,'2','1','1','0','1','2021-06-04 07:07:17','2021-06-04 12:37:17'),(1653,89,'transactions approved will be subject to 100 per cent audit by','','multi','single','','','1','19',NULL,'3','1','1','0','1','2021-06-04 05:44:55','2021-06-04 11:14:55'),(1654,89,'Which exports are freely exportable item allowed without any limit.','','multi','single','','','1','20',NULL,'3','1','1','0','1','2021-06-04 05:51:10','2021-06-04 11:21:10'),(1655,89,'Application for which are  restricted for export, to DGFT as per ANF-2Q','','multi','single','','','1','20',NULL,'1','1','1','0','1','2021-06-04 05:00:25','2021-06-04 10:30:25'),(1656,89,'Including edible items, not exceeding how much in a licensing year.','','multi','single','','','1','21',NULL,'1','1','1','0','1','2021-06-04 05:29:11','2021-06-04 10:59:11'),(1657,89,'Items restricted for exports in ITC (HS) require','','multi','single','','','1','21',NULL,'1','1','1','0','1','2021-06-04 05:31:47','2021-06-04 11:01:47'),(1658,89,'What is the full form of ORM?','','multi','single','','','1','22',NULL,'2','1','1','0','1','2021-06-05 04:18:07','2021-06-05 09:48:07'),(1659,89,'What is the full form of  IDPMS?','','multi','single','','','1','22',NULL,'1','1','1','0','1','2021-06-05 04:18:44','2021-06-05 09:48:44'),(1660,89,'Any other benefit upload on DGFT’s website RCMC, unless specifically exempted under','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-04 04:59:48','2021-06-04 10:29:48'),(1661,89,'CRES issued by Spices Board shall be treated as','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-04 05:06:07','2021-06-04 10:36:07'),(1662,89,'EDF approval for export of goods for','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-04 05:09:34','2021-06-04 10:39:34'),(1663,89,'AD may allow remittances towards initial expenses up to','','multi','single','','','1','24',NULL,'2','1','1','0','1','2021-06-04 04:48:04','2021-06-04 10:18:04'),(1664,89,'For recurring expenses, remittances up to how much of  annual sales/income?','','multi','single','','','1','24',NULL,'4','1','1','0','1','2021-06-04 05:22:45','2021-06-04 10:52:45'),(1665,89,'AD may acquire which property for business & residential purpose of staff','','multi','single','','','1','24',NULL,'2','1','1','0','1','2021-06-04 04:46:30','2021-06-04 10:16:30'),(1666,89,'Which statement showing receipts under ‘off-site’ & ‘on-site’ contracts undertaken by overseas office','','multi','single','','','1','24',NULL,'2','1','1','0','1','2021-06-04 06:57:19','2021-06-04 12:27:19'),(1667,89,'Exporters’ present exports documents after how many days from date of export','','multi','single','','','1','24',NULL,'1','1','1','0','1','2021-06-05 04:02:11','2021-06-05 09:32:11'),(1668,89,'Shipping documents, once submitted to','','multi','single','','','1','24',NULL,'2','1','1','0','1','2021-06-04 05:43:26','2021-06-04 11:13:26'),(1669,89,'AD may deliver how many negotiable copy of the Bill of Lading to Master of the carrying vessel','','multi','single','','','1','25',NULL,'4','1','1','0','1','2021-06-04 04:50:42','2021-06-04 10:20:42'),(1670,88,'<p>23 Merchanting Trade</p>','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227490731622749073.mp4','','1','23','Merchanting Trade','1','2','1','0','1','2021-06-04 01:07:53','2021-11-09 13:23:53'),(1671,89,'Which of following should normally dispatch shipping documents to overseas branches/correspondents expeditiously','','multi','single','','','1','26',NULL,'1','1','1','0','1','2021-06-04 05:51:36','2021-06-04 11:21:36'),(1672,89,'Advance payment / LC received for full value & contract/LC provides for dispatch of documents direct to which of the following','','multi','single','','','1','26',NULL,'3','1','1','0','1','2021-06-04 04:56:11','2021-06-04 10:26:11'),(1673,89,'Whom AD may permit to dispatch export documents','','multi','single','','','1','26',NULL,'3','1','1','0','1','2021-06-04 07:00:13','2021-06-04 12:30:13'),(1674,89,'Duplicate of EDF submitted to whom for monitoring purposes','','multi','single','','','1','26',NULL,'3','1','1','0','1','2021-06-04 05:08:56','2021-06-04 10:38:56'),(1675,89,'From the date of shipment of export within how many days Duplicate of EDF submitted','','multi','single','','','1','26',NULL,'4','1','1','0','1','2021-06-04 05:23:18','2021-06-04 10:53:18'),(1676,89,'Exporter’s account with AD is fully compliant with which of the following','','multi','single','','','1','26',NULL,'3','1','1','0','1','2021-06-04 05:17:20','2021-06-04 10:47:20'),(1677,89,'Undertaking from exporter on duplicate of which forms','','multi','single','','','1','27',NULL,'1','1','1','0','1','2021-06-04 05:46:55','2021-06-04 11:16:55'),(1678,89,'Least value for which bill was initially drawn','','multi','single','','','1','27',NULL,'1','1','1','0','1','2021-06-04 05:33:38','2021-06-04 11:03:38'),(1679,89,'Goods exported on which  basis','','multi','single','','','1','28',NULL,'1','1','1','0','1','2021-06-04 05:23:58','2021-06-04 10:53:58'),(1680,89,'Who forwarding documents to overseas branch','','multi','single','','','1','28',NULL,'2','1','1','0','1','2021-06-05 04:14:56','2021-06-05 09:44:56'),(1681,89,'Landing charges, warehouse rent, handling charges, etc. & remit the net proceeds to which of the following','','multi','single','','','1','28',NULL,'1','1','1','0','1','2021-06-04 05:32:35','2021-06-04 11:02:35'),(1682,89,'Which export Account sales should be verified by AD','','multi','single','','','1','28',NULL,'1','1','1','0','1','2021-06-04 05:50:47','2021-06-04 11:20:47'),(1683,89,'Who may show value of unsold goods as 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following  is not required.','','multi','single','','','1','28',NULL,'1','1','1','0','1','2021-06-04 05:02:57','2021-06-04 10:32:57'),(1689,89,'AD may extend period of realization of export proceeds beyond stipulated period of realization, up to how many months','','multi','single','','','1','29',NULL,'2','1','1','0','1','2021-06-04 04:52:10','2021-06-04 10:22:10'),(1690,89,'Who submits a declaration that proceeds will be realized during extended period','','multi','single','','','1','29',NULL,'2','1','1','0','1','2021-06-04 07:06:40','2021-06-04 12:36:40'),(1691,89,'Which of the following must ensure insurance claim is made as soon as loss is known.','','multi','single','','','1','30',NULL,'1','1','1','0','1','2021-06-04 06:54:43','2021-06-04 12:24:43'),(1692,89,'Who may advised to surrender proportionate export incentives, if any, received by him?','','multi','single','','','1','31',NULL,'1','1','1','0','1','2021-06-04 07:01:27','2021-06-04 12:31:27'),(1693,89,'Self “write-off” by an which of the following','','multi','single','','','1','32',NULL,'1','1','1','0','1','2021-06-04 05:41:58','2021-06-04 11:11:58'),(1694,89,'Write-off” by Authorized Dealer Bank-','','multi','single','','','1','32',NULL,'3','1','1','0','1','2021-06-04 07:08:48','2021-06-04 12:38:48'),(1695,89,'Who are not traceable over a reasonably long period of time.','','multi','single','','','1','32',NULL,'1','1','1','0','1','2021-06-04 06:58:42','2021-06-04 12:28:42'),(1696,89,'Undrawn balance not exceeding','','multi','single','','','1','32',NULL,'2','1','1','0','1','2021-06-04 05:47:25','2021-06-04 11:17:25'),(1697,89,'AD to obtain documents evidencing surrender of which incentives','','multi','single','','','1','32',NULL,'1','1','1','0','1','2021-06-05 04:17:09','2021-06-05 09:47:09'),(1698,89,'Write off in cases of payment of claims by','','multi','single','','','1','32',NULL,'1','1','1','0','1','2021-06-04 07:09:25','2021-06-04 12:39:25'),(1699,89,'Who is as per the Foreign Trade Policy in force','','multi','single','','','1','33',NULL,'1','1','1','0','1','2021-06-04 06:59:43','2021-06-04 12:29:43'),(1700,89,'Exchange Control copies of Bills of Entry for home consumption submitted by','','multi','single','','','1','33',NULL,'1','1','1','0','1','2021-06-04 05:12:51','2021-06-04 10:42:51'),(1701,89,'Transactions with which countries kept outside arrangement','','multi','single','','','1','33',NULL,'2','1','1','0','1','2021-06-04 05:45:46','2021-06-04 11:15:46'),(1702,89,'Who may allow payment of commission, by remittance / deduction from invoice value','','multi','single','','','1','34',NULL,'1','1','1','0','1','2021-06-04 07:02:00','2021-06-04 12:32:00'),(1703,89,'AD may allow under counter trade arrangement through','','multi','single','','','1','34',NULL,'1','1','1','0','1','2021-06-04 04:49:22','2021-06-04 10:19:22'),(1704,89,'Who may consider requests for refund of export proceeds of goods exported from India & being re-imported on account of poor quality.','','multi','single','','','1','35',NULL,'1','1','1','0','1','2021-06-04 07:03:29','2021-06-04 12:33:29'),(1705,89,'Exporter that goods will be re-imported within how much  from date of remittance','','multi','single','','','1','35',NULL,'1','1','1','0','1','2021-06-04 05:16:35','2021-06-04 10:46:35'),(1706,90,'1 INTRODUCTION OF PROGRAMME.','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227972111622797211.mp4','','1','1',NULL,'1','2','1','0','1','2021-06-04 14:30:12','2021-06-04 14:30:12'),(1707,90,'2 INTRODUCTION OF INSTRUCTOR','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227972741622797274.mp4','','1','2',NULL,'1','2','1','0','1','2021-06-28 06:28:16','2021-06-28 11:58:16'),(1708,90,'6 TRANSACTIONS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227975411622797541.mp4','','1','6',NULL,'1','2','1','0','1','2021-06-04 14:35:42','2021-06-04 14:35:42'),(1709,90,'8 FACTORS AFFECTING EXCHANGE RATES','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227976231622797623.mp4','','1','8',NULL,'1','2','1','0','1','2021-06-04 14:37:04','2021-06-04 14:37:04'),(1710,90,'10 FORWARD CONTRACTS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227976741622797674.mp4','','1','10',NULL,'1','2','1','0','1','2021-06-05 11:58:14','2021-06-05 17:28:14'),(1711,90,'12 SWAPS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227977601622797760.mp4','','1','12',NULL,'1','2','1','0','1','2021-06-04 14:39:20','2021-06-04 14:39:20'),(1712,91,'1 INTRODUCTION OF PROGRAMME.','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227984031622798403.mp4','','1','1',NULL,'1','2','1','0','1','2021-06-04 09:20:03','2021-06-04 14:50:03'),(1713,91,'2 INTRODUCTION OF INSTRUCTOR','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16227983701622798370.mp4','','1','2',NULL,'1','2','1','0','1','2021-06-28 06:31:26','2021-06-28 12:01:26'),(1714,91,'Who said “A customer is the most important visitor on our premises. He is not dependent on us. We are dependent on him. He is not an interruption in our work...............\"','','single','single','','','1','3',NULL,'1','1','1','0','1','2021-06-04 12:13:44','2021-06-04 17:43:44'),(1715,91,'What is a factor that helps you stand out of the competition?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-04 12:18:32','2021-06-04 17:48:32'),(1716,91,'Who are the most important people for any organization?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-04 12:21:16','2021-06-04 17:51:16'),(1717,91,'What Satisfied customers are more likely to share?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-08 04:49:27','2021-06-08 10:19:27'),(1718,91,'What can bolster all departments of your company and also help achieve their respective goals?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-08 04:53:03','2021-06-08 10:23:03'),(1719,91,'In a recent survey, how many percentage of people said that they found customer satisfaction a useful 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CLV?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-08 05:08:16','2021-06-08 10:38:16'),(1725,91,'What is the full of ROI?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-08 05:08:55','2021-06-08 10:38:55'),(1726,91,'What is a beneficiary of high levels of both customer satisfaction and retention?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-08 05:10:50','2021-06-08 10:40:50'),(1727,91,'Why customers are important?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-08 05:12:54','2021-06-08 10:42:54'),(1728,91,'<p>What increases with good customer service?</p>','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-08 05:15:26','2022-01-26 10:18:42'),(1729,91,'Who is the foundation of any business\' success?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-08 05:17:21','2021-06-08 10:47:21'),(1730,90,'\"FOREX\" stands for ?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-05 10:20:55','2021-06-05 15:50:55'),(1731,90,'Currency symbols are codified into _______ letters.','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-05 11:44:51','2021-06-05 17:14:51'),(1732,90,'The abbreviation \"CHF\" stands for ?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-05 12:10:07','2021-06-05 17:40:06'),(1733,90,'Which is the world\'s most dominant currency ?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-05 12:27:13','2021-06-05 17:57:13'),(1734,90,'Maintaining a Foreign Currency Account is helpful to -','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-05 11:59:40','2021-06-05 17:29:40'),(1735,90,'What does EMEs stand for in Foreign Exchange ?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-07 07:03:08','2021-06-07 12:33:08'),(1736,90,'India\'s Foreign Exchange Rate system is ?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-05 11:54:31','2021-06-05 17:24:31'),(1737,90,'\"Yen\" is the currency of which country ?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-05 10:21:48','2021-06-05 15:51:48'),(1738,90,'What is the market turn over of USA ?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-05 12:20:47','2021-06-05 17:50:47'),(1739,90,'Currency prices are affected by which of the following ?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-05 11:43:43','2021-06-05 17:13:43'),(1740,90,'Who among the following acts as an intermediary between Foreign Exchange Supply and Demand ?','','multi','single','','','1','4',NULL,'1','1','1','0','1','2021-06-05 12:31:10','2021-06-05 18:01:10'),(1741,90,'Which city is the largest centre for Trading ?','','multi','single','','','1','4',NULL,'3','1','1','0','1','2021-06-05 12:25:40','2021-06-05 17:55:40'),(1742,90,'OTC market stands for ?','','multi','single','','','1','4',NULL,'2','1','1','0','1','2021-06-05 12:03:59','2021-06-05 17:33:59'),(1743,90,'Currency is said to be convertible if the person holding it can change it in any other currency.','','multi','single','','','1','4',NULL,'1','1','1','0','1','2021-06-05 11:41:36','2021-06-05 17:11:36'),(1744,90,'What is the root cause of Foreign Exchange ?','','multi','single','','','1','4',NULL,'2','1','1','0','1','2021-06-05 12:21:20','2021-06-05 17:51:20'),(1745,90,'Business hours in New York are from ______ to _______EST. ?','','multi','single','','','1','4',NULL,'3','1','1','0','1','2021-06-05 10:29:20','2021-06-05 15:59:20'),(1746,90,'Which is the third largest center for Trading ?','','multi','single','','','1','4',NULL,'3','1','1','0','1','2021-06-05 12:26:06','2021-06-05 17:56:06'),(1747,90,'Which is the third largest center for Trading ?','','multi','single','','','1','4',NULL,'3','1','1','1','1','2021-06-07 07:09:00','2021-06-07 12:39:00'),(1748,90,'What does 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as?','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-05 12:02:50','2021-06-05 17:32:50'),(1755,90,'FX spot is the short form used for?','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-07 07:16:26','2021-06-07 12:46:26'),(1756,90,'The Acronym TOM stands for ?','','multi','single','','','1','5',NULL,'3','1','1','0','1','2021-06-05 12:10:33','2021-06-05 17:40:33'),(1757,90,'The exchange rate at which the transaction is done is called?','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-05 12:13:00','2021-06-05 17:43:00'),(1758,90,'The exchange rate at which the transaction is done is called?','','multi','single','','','1','5',NULL,'2','1','1','1','1','2021-06-07 08:15:15','2021-06-07 13:45:15'),(1759,90,'What is the value of 1 USD in Indian Currency ?','','multi','single','','','1','6',NULL,'4','1','1','0','1','2021-06-05 12:21:47','2021-06-05 17:51:47'),(1760,90,'In Foreign Exchange, how many types of transactions are dealt by Banks ?','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-07 07:21:29','2021-06-07 12:51:29'),(1761,90,'In India rates are quoted in _______ term.','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-05 11:56:06','2021-06-05 17:26:06'),(1762,90,'A market outside the International borders of company\'s country of Citizenship, is called','','multi','single','','','1','6',NULL,'3','1','1','0','1','2021-06-07 07:18:48','2021-06-07 12:48:48'),(1763,90,'Sale of Foreign Exchange to Customers of Bank is called Merchant Transaction.','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-05 12:07:53','2021-06-05 17:37:53'),(1764,90,'What does INR stands for in Currency ?','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-05 12:19:34','2021-06-05 17:49:34'),(1765,90,'When Banker sales Foreign Currency it is ___transaction for Banker and ____transaction for 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12:58:37'),(1771,90,'_________ Bank is Market Maker.','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-05 12:35:47','2021-06-05 18:05:47'),(1772,90,'Who is a Market Maker ?','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-05 12:32:22','2021-06-05 18:02:22'),(1773,90,'1 Indian Rupee equals ________United States Dollar.','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-05 10:22:34','2021-06-05 15:52:34'),(1774,90,'Buying Rate is also called as ?','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-05 10:29:55','2021-06-05 15:59:55'),(1775,90,'Spot Market Exchange Rate is also known as Base Rate.','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-05 12:09:02','2021-06-05 17:39:02'),(1776,90,'Choose the factor that affect Exchange Rates ?','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-05 11:42:24','2021-06-05 17:12:24'),(1777,90,'Economic Policy is also known as ?','','multi','single','','','1','8',NULL,'3','1','1','0','1','2021-06-05 11:47:24','2021-06-05 17:17:24'),(1778,90,'Future price >Spot price.','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-05 11:52:37','2021-06-05 17:22:37'),(1779,90,'Prices of essential commodities affect Exchange Rates.','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-07 07:47:02','2021-06-07 13:17:02'),(1780,90,'What does Inflation stand for?','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-07 07:46:07','2021-06-07 13:16:07'),(1781,90,'Account that a bank holds in a Foreign Currency in another bank is known as?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-05 10:11:21','2021-06-05 15:41:21'),(1782,90,'Trade Control regulates Import and Export of Goods','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-05 12:16:26','2021-06-05 17:46:26'),(1783,90,'Exchange Control is supplemented by________.','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-05 11:49:29','2021-06-05 17:19:29'),(1784,90,'What does TT buying rates mean?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-07 07:50:23','2021-06-07 13:20:23'),(1785,90,'In Bill Buying rates Premium is added to Spot rate.','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-07 07:53:44','2021-06-07 13:23:44'),(1786,90,'In TT buying rate , TT stands for ?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-05 11:58:48','2021-06-05 17:28:48'),(1787,90,'On which Maxim does Bill Buying rate work?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-07 07:51:58','2021-06-07 13:21:58'),(1788,90,'Bill Selling Rates are applied for ?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-05 10:28:44','2021-06-05 15:58:44'),(1789,90,'Which of the following is the form of Derivative Product ?','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-05 12:27:57','2021-06-05 17:57:57'),(1790,90,'Simultaneous Buying and Selling of same Currency for different future dates is known as ?','','multi','single','','','1','10',NULL,'3','1','1','0','1','2021-06-05 12:08:23','2021-06-05 17:38:23'),(1791,90,'Premium is an amount to be paid for a contract of Insurance.','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-05 12:06:58','2021-06-05 17:36:58'),(1792,90,'________ Currency is at Premium in Forward Market.','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-05 12:35:14','2021-06-05 18:05:14'),(1793,90,'Forward Contracts may create a loss to Bank due to exchange rate differential.','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-05 11:51:27','2021-06-05 17:21:27'),(1794,90,'______is all about taking Financial risks in hope of making profit.','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-05 12:32:56','2021-06-05 18:02:56'),(1795,90,'Premium Currency is cheaper and Discount Currency is dearer.','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-05 12:05:27','2021-06-05 17:35:27'),(1796,90,'Active Trading is also known as ?','','multi','single','','','1','10',NULL,'3','1','1','0','1','2021-06-05 10:23:17','2021-06-05 15:53:17'),(1797,90,'Investing is about minimizing the risk and maximizing return.','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-05 11:59:13','2021-06-05 17:29:13'),(1798,90,'When was National Stock Exchange of India Limited founded ?','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-05 12:24:33','2021-06-05 17:54:33'),(1799,90,'In OTC derivatives, OTC stands for ?','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-07 08:01:38','2021-06-07 13:31:38'),(1800,90,'Market movement is not necessary in Derivative Market .','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-05 12:00:47','2021-06-05 17:30:47'),(1801,90,'Example of Derivative Security is -','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-05 11:48:54','2021-06-05 17:18:54'),(1802,90,'Example of Derivative Security is -','','multi','single','','','1','11',NULL,'2','1','1','1','1','2021-06-07 08:04:41','2021-06-07 13:34:41'),(1803,90,'Using futures contracts to transfer Price risk is known as which of the following ?','','multi','single','','','1','11',NULL,'3','1','1','0','1','2021-06-05 12:17:02','2021-06-05 17:47:02'),(1804,90,'The effect of Speculation on exchange rate is -','','multi','single','','','1','11',NULL,'3','1','1','0','1','2021-06-05 12:12:32','2021-06-05 17:42:32'),(1805,90,'Freight Derivatives can include -','','multi','single','','','1','11',NULL,'4','1','1','0','1','2021-06-05 11:52:06','2021-06-05 17:22:06'),(1806,90,'In Exchange, Hedging means :','','multi','single','','','1','11',NULL,'4','1','1','0','1','2021-06-05 11:55:09','2021-06-05 17:25:09'),(1807,90,'Exchange is also known as Dealing Bourse.','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-05 11:50:18','2021-06-05 17:20:18'),(1808,90,'PITS is also known as ?','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-05 12:04:59','2021-06-05 17:34:59'),(1809,90,'Who among the following holds the position for a day to a week or month ?','','multi','single','','','1','11',NULL,'3','1','1','0','1','2021-06-05 12:31:42','2021-06-05 18:01:42'),(1810,90,'______ options can be exercised only on Maturity date.','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-05 12:34:38','2021-06-05 18:04:38'),(1811,90,'Philadelphia Stock Exchange is the oldest Stock Exchange in the United States.','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-05 12:04:32','2021-06-05 17:34:32'),(1812,90,'Which option gives Holder right to sell?','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-05 12:30:12','2021-06-05 18:00:12'),(1813,90,'Down-and-in Option is a type of Knock-in barrier Option.','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-05 11:46:44','2021-06-05 17:16:44'),(1814,90,'Interest rate Swap which involves exchange of two floating  rate financial instruments, is known as ?','','multi','single','','','1','12',NULL,'3','1','1','0','1','2021-06-07 08:06:53','2021-06-07 13:36:53'),(1815,90,'The Swap Transaction involves sale and purchase of same Currency but different Maturities.','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-05 12:15:44','2021-06-05 17:45:44'),(1816,90,'A Plain Vanilla Swap  includes which of the following ?','','multi','single','','','1','12',NULL,'4','1','1','0','1','2021-06-05 10:26:35','2021-06-05 15:56:35'),(1817,90,'Swaps allows companies to revise their debt conditions to take advantage of current market conditions.','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-05 12:09:41','2021-06-05 17:39:41'),(1818,90,'Interest rate Swap is not an Interest rate Derivative','','multi','single','','','1','12',NULL,'2','1','1','0','1','2021-06-05 11:56:42','2021-06-05 17:26:42'),(1819,90,'Financial Swaps are used by following organizations ?','','multi','single','','','1','12',NULL,'4','1','1','0','1','2021-06-05 11:50:47','2021-06-05 17:20:47'),(1820,90,'A Currency Swap Bank is usually ?','','multi','single','','','1','12',NULL,'3','1','1','0','1','2021-06-05 10:25:02','2021-06-05 15:55:02'),(1821,90,'An Interest rate floor in Currency Swaps sets -','','multi','single','','','1','12',NULL,'3','1','1','0','1','2021-06-05 10:26:01','2021-06-05 15:56:01'),(1822,90,'Currency Swaps involve ?','','multi','single','','','1','12',NULL,'3','1','1','0','1','2021-06-05 11:44:18','2021-06-05 17:14:18'),(1823,90,'Interest Rate Swaps involve Counterparties who want to -','','multi','single','','','1','12',NULL,'2','1','1','0','1','2021-06-05 11:57:48','2021-06-05 17:27:48'),(1824,90,'3 WHAT IS FOREIGN EXCHANGE','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16228969231622896923.mp4','','1','3',NULL,'1','2','1','0','1','2021-06-05 18:12:03','2021-06-05 18:12:03'),(1825,90,'4 CONVERTIBILITY AND GLOBAL FOREX TREASURY','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16228973751622897375.mp4','','1','4',NULL,'1','2','1','0','1','2021-06-05 18:19:36','2021-06-05 18:19:36'),(1826,90,'5 RATE OF EXCHANGE AND FOREX MARKET IN INDIA','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16228981361622898136.mp4','','1','5',NULL,'1','2','1','0','1','2021-06-05 18:32:17','2021-06-05 18:32:17'),(1827,90,'7 PRINCIPLES FOR EXCHANGE RATES','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16228985321622898532.mp4','','1','7',NULL,'1','2','1','0','1','2021-06-05 18:38:53','2021-06-05 18:38:53'),(1828,90,'9 EXCHANGE CONTROL AND TRADE CONTROL','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16228988181622898818.mp4','','1','9',NULL,'1','2','1','0','1','2021-06-05 18:43:39','2021-06-05 18:43:39'),(1829,90,'10 FORWARD CONTRACTS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16228990921622899092.mp4','','1','10',NULL,'1','2','1','1','1','2021-06-07 07:57:49','2021-06-07 13:27:49'),(1830,90,'11 DERIVATIVE PRODUCTS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16228993731622899373.mp4','','1','11',NULL,'1','2','1','0','1','2021-06-05 18:52:53','2021-06-05 18:52:53'),(1831,92,'1 Introduction','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229546471622954647.mp4','','1','1',NULL,'1','2','1','0','1','2021-06-06 10:14:08','2021-06-06 10:14:08'),(1832,92,'2  Introduction of Instructor','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229548981622954898.mp4','','1','2',NULL,'1','2','1','0','1','2021-06-28 06:28:54','2021-06-28 11:58:54'),(1833,92,'3 Sources of Finance','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229550001622955000.mp4','','1','3',NULL,'1','2','1','0','1','2021-06-06 10:20:01','2021-06-06 10:20:01'),(1834,92,'4 Fund based facilities','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229550991622955099.mp4','','1','4',NULL,'1','2','1','0','1','2021-06-06 10:21:39','2021-06-06 10:21:39'),(1835,92,'5 Non-fund-based 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for consideration','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229557031622955702.mp4','','1','9',NULL,'1','2','1','0','1','2021-06-06 10:31:44','2021-06-06 10:31:44'),(1840,92,'10 Types of financial arrangements','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229558371622955837.mp4','','1','10',NULL,'1','2','1','0','1','2021-06-06 05:03:58','2021-06-06 10:33:58'),(1841,92,'12 Packing credit','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229559841622955983.mp4','','1','12',NULL,'1','2','1','0','1','2021-06-06 10:36:24','2021-06-06 10:36:24'),(1842,92,'13 Pre-shipment finance','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229560251622956025.mp4','','1','13',NULL,'1','2','1','0','1','2021-06-06 10:37:06','2021-06-06 10:37:06'),(1843,92,'14 Bank 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Facilities','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229564481622956447.mp4','','1','20',NULL,'1','2','1','0','1','2021-06-06 10:44:08','2021-06-06 10:44:08'),(1848,92,'21 External commercial borrowings (ECB)','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229564941622956494.mp4','','1','21',NULL,'1','2','1','0','1','2021-06-06 10:44:55','2021-06-06 10:44:55'),(1849,92,'22 Forms of ECB','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229567351622956735.mp4','','1','22',NULL,'1','2','1','0','1','2021-06-06 05:18:55','2021-06-06 10:48:55'),(1850,92,'23 Lending in foreign currency by an A.D','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229565901622956590.mp4','','1','23',NULL,'1','2','1','0','1','2021-06-06 10:46:30','2021-06-06 10:46:30'),(1851,92,'24 ECGC','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229566451622956645.mp4','','1','24',NULL,'1','2','1','0','1','2021-06-06 10:47:25','2021-06-06 10:47:25'),(1852,92,'25 Subsidiary services offered by Indian banks','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16229566811622956681.mp4','','1','25',NULL,'1','2','1','0','1','2021-06-06 10:48:01','2021-06-06 10:48:01'),(1853,92,'Which bank in India offers short term working finance?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-06 15:51:53','2021-06-06 15:51:53'),(1854,92,'Sanction letter is usually sanctioned for?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-06 15:53:23','2021-06-06 15:53:23'),(1855,92,'Sanction letter is issued by ?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-06 15:54:49','2021-06-06 15:54:49'),(1856,92,'Fixed capital loans are provided on?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-06 15:55:59','2021-06-06 15:55:59'),(1857,92,'Consumer durable loans are provided on?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-06 15:57:12','2021-06-06 15:57:12'),(1858,92,'Inventory finance is also known as?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-06 15:58:59','2021-06-06 15:58:59'),(1859,92,'Which of the following comes under fund based facilities?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-06 16:00:11','2021-06-06 16:00:11'),(1860,92,'In pre-shipment finance, packing credit is provided in Indian as well as which currency?','','multi','single','','','1','4',NULL,'3','1','1','0','1','2021-06-06 16:01:39','2021-06-06 16:01:39'),(1861,92,'Which of the following is provided for international business?','','multi','single','','','1','4',NULL,'4','1','1','0','1','2021-06-06 16:02:57','2021-06-06 16:02:57'),(1862,92,'Foreign bill can be 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by?','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-06 16:12:42','2021-06-06 16:12:42'),(1869,92,'LC bills remaining unpaid beyond a particular period are?','','multi','single','','','1','6',NULL,'3','1','1','0','1','2021-06-06 16:13:35','2021-06-06 16:13:35'),(1870,92,'Import bill collection is done by?','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-06 16:14:37','2021-06-06 16:14:37'),(1871,92,'What is LC bill?','','multi','single','','','1','6',NULL,'3','1','1','0','1','2021-06-06 16:15:45','2021-06-06 16:15:45'),(1872,92,'Crystallization is a process used for?','','multi','single','','','1','6',NULL,'4','1','1','0','1','2021-06-06 16:16:41','2021-06-06 16:16:41'),(1873,92,'Which bank is associated with export trade services?','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-06 16:18:37','2021-06-06 16:18:37'),(1874,92,'The transfer of export documentary letter of  credit is done by','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-06 16:19:44','2021-06-06 16:19:44'),(1875,92,'The purchase/discount/negotiation of export bill is done by?','','multi','single','','','1','7',NULL,'3','1','1','0','1','2021-06-06 16:20:49','2021-06-06 16:20:49'),(1876,92,'In respect of export services. Which activities are done by bank?','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-06 16:22:10','2021-06-06 16:22:10'),(1877,92,'Which of the document comes under off balance sheet activities?','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-06 16:23:49','2021-06-06 16:23:49'),(1878,92,'What are derivative transactions?','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-11 06:26:28','2021-06-11 11:56:28'),(1879,92,'What are the examples of derivatives','','multi','single','','','1','8',NULL,'3','1','1','0','1','2021-06-11 06:25:40','2021-06-11 11:55:40'),(1880,92,'What are Collateral?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-06 16:28:00','2021-06-06 16:28:00'),(1881,92,'Which of the following can be the example of collateral?','','multi','single','','','1','9',NULL,'4','1','1','0','1','2021-06-06 16:29:41','2021-06-06 16:29:41'),(1882,92,'Mortgage is an example of?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-11 06:30:29','2021-06-11 12:00:29'),(1883,92,'Mortgage is charged over?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-06 16:31:52','2021-06-06 16:31:52'),(1884,92,'How many types of mortgage are there','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-06 16:32:58','2021-06-06 16:32:58'),(1885,92,'What is usufructuary mortgage?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-06 16:34:42','2021-06-06 16:34:42'),(1886,92,'Which of the following, does not come under any of the mortgage','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-06 16:36:00','2021-06-06 16:36:00'),(1887,92,'How many types of financial arrangement are there?','','multi','single','','','1','10',NULL,'3','1','1','0','1','2021-06-06 16:37:31','2021-06-06 16:37:31'),(1888,92,'What is bid rate?','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-06 16:38:46','2021-06-06 16:38:46'),(1889,92,'The export credit guarantee corporation  of India is established by?','','multi','single','','','1','10',NULL,'3','1','1','0','1','2021-06-06 16:39:48','2021-06-06 16:39:48'),(1890,92,'What is offer rate?','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-06 16:41:16','2021-06-06 16:41:16'),(1891,92,'Term loan, overdraft, equipment leasing are few example of ?','','multi','single','','','1','10',NULL,'3','1','1','0','1','2021-06-06 16:42:19','2021-06-06 16:42:19'),(1892,92,'Does every exporter get export finance?','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-06 16:43:36','2021-06-06 16:43:36'),(1893,92,'What is LIBID?','','multi','single','','','1','10',NULL,'4','1','1','0','1','2021-06-06 16:45:12','2021-06-06 16:45:12'),(1894,92,'Working capital finance is needed by?','','multi','single','','','1','11',NULL,'4','1','1','0','1','2021-06-06 16:46:31','2021-06-06 16:46:31'),(1895,92,'Who purchases ready made goods, arrange repacking and ship?','','multi','single','','','1','11',NULL,'1','1','1','0','1','2021-06-06 16:47:26','2021-06-06 16:47:26'),(1896,92,'Export working capital finances are generally secured by?','','multi','single','','','1','11',NULL,'3','1','1','0','1','2021-06-06 16:48:17','2021-06-06 16:48:17'),(1897,92,'Pre-shipment finance provided by the bank to the exporter are for activities such as?','','multi','single','','','1','11',NULL,'4','1','1','0','1','2021-06-06 16:49:14','2021-06-06 16:49:14'),(1898,92,'Bank grants pre-shipment finance in the form of?','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-06 16:51:52','2021-06-06 16:51:52'),(1899,92,'Working capital finance can be drawn by lodgement of?','','multi','single','','','1','11',NULL,'3','1','1','0','1','2021-06-06 16:53:05','2021-06-06 16:53:05'),(1900,92,'What is the meaning of disbursement?','','multi','single','','','1','12',NULL,'2','1','1','0','1','2021-06-06 16:54:43','2021-06-06 16:54:43'),(1901,92,'What does packing credit means?','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-06 16:55:42','2021-06-06 16:55:42'),(1902,92,'While disbursing, bank ensures that the exporter is able to_____the advance by export proceeds?','','multi','single','','','1','12',NULL,'3','1','1','0','1','2021-06-06 16:56:36','2021-06-06 16:56:36'),(1903,92,'Packing credit should be settled in______period?','','multi','single','','','1','12',NULL,'4','1','1','0','1','2021-06-06 16:57:36','2021-06-06 16:57:36'),(1904,92,'Pre-shipment finance are?','','multi','single','','','1','13',NULL,'1','1','1','0','1','2021-06-06 16:58:44','2021-06-06 16:58:44'),(1905,92,'IF bank grants pre-shipment finance, it is usually required to sanction______also?','','multi','single','','','1','13',NULL,'2','1','1','0','1','2021-06-06 16:59:44','2021-06-06 16:59:44'),(1906,92,'Interest charged on pre-shipment finance, is charged____?','','multi','single','','','1','13',NULL,'3','1','1','0','1','2021-06-06 17:00:52','2021-06-06 17:00:52'),(1907,92,'Pre-shipment finance can be liquidated by lodgment of ?','','multi','single','','','1','13',NULL,'2','1','1','0','1','2021-06-06 17:02:04','2021-06-06 17:02:04'),(1908,92,'What is FIFO system?','','multi','single','','','1','14',NULL,'2','1','1','0','1','2021-06-06 17:03:33','2021-06-06 17:03:33'),(1909,92,'What is LIFO system?','','multi','single','','','1','14',NULL,'2','1','1','0','1','2021-06-06 17:04:52','2021-06-06 17:04:52'),(1910,92,'Which of the following is a discretionary power of bank?','','multi','single','','','1','14',NULL,'4','1','1','0','1','2021-06-06 17:06:05','2021-06-06 17:06:05'),(1911,92,'Who is expected to liquidate pre-shipment finance?','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-06 17:08:30','2021-06-06 17:08:30'),(1912,92,'What helps to liquidate pre-shipment finance?','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-06 17:09:41','2021-06-06 17:09:41'),(1913,92,'For post-shipment finance, interest charged is on _____basis?','','multi','single','','','1','15',NULL,'3','1','1','0','1','2021-06-06 17:11:37','2021-06-06 17:11:37'),(1914,92,'Which of the following comes under post-shipment finance?','','multi','single','','','1','15',NULL,'4','1','1','0','1','2021-06-06 17:13:42','2021-06-06 17:13:42'),(1915,92,'Post-shipment finance is _____?','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-06 17:15:04','2021-06-06 17:15:04'),(1916,92,'Account may be operated on running account basis as in the case of ?','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-07 11:12:19','2021-06-07 11:12:19'),(1917,92,'Can exporter avail pre-shipment finance, initially without lodgement of LC?','','multi','single','','','1','16',NULL,'2','1','1','0','1','2021-06-07 11:14:05','2021-06-07 11:14:05'),(1918,92,'What is the reasonable time within which documents should be lodged?','','multi','single','','','1','16',NULL,'3','1','1','0','1','2021-06-07 11:15:40','2021-06-07 11:15:40'),(1919,92,'Exporter’s credit-worthiness & limits are____?','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-07 11:17:16','2021-06-07 11:17:16'),(1920,92,'Negotiations can be done on post-shipment finance on_____?','','multi','single','','','1','17',NULL,'2','1','1','0','1','2021-06-07 11:18:15','2021-06-07 11:18:15'),(1921,92,'Bill remaining overdue beyond a reasonable period is considered as?','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-07 11:19:53','2021-06-07 11:19:53'),(1922,92,'Overdue advances attracts_____?','','multi','single','','','1','18',NULL,'2','1','1','0','1','2021-06-07 11:20:53','2021-06-07 11:20:53'),(1923,92,'When is exchange fluctuation rate come into play?','','multi','single','','','1','18',NULL,'3','1','1','0','1','2021-06-07 11:22:08','2021-06-07 11:22:08'),(1924,92,'For over due bills beyond limit, bank crystallizes______liability?','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-07 11:23:09','2021-06-07 11:23:09'),(1925,92,'Bank issues gold card for?','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-07 11:24:13','2021-06-07 11:24:13'),(1926,92,'What is the benefit of having a gold card?','','multi','single','','','1','19',NULL,'2','1','1','0','1','2021-06-07 11:25:03','2021-06-07 11:25:03'),(1927,92,'Who lays down criteria for gold card?','','multi','single','','','1','19',NULL,'3','1','1','0','1','2021-06-07 11:25:53','2021-06-07 11:25:53'),(1928,92,'Who has the authority to blacklist exporters?','','multi','single','','','1','19',NULL,'1','1','1','0','1','2021-06-07 11:26:52','2021-06-07 11:26:52'),(1929,92,'Can the blacklisted exporters claim gold card?','','multi','single','','','1','19',NULL,'2','1','1','0','1','2021-06-07 11:28:06','2021-06-07 11:28:06'),(1930,92,'Banks provide facilities such as___?','','multi','single','','','1','20',NULL,'4','1','1','0','1','2021-06-07 11:31:39','2021-06-07 11:31:39'),(1931,92,'For meeting urgent payment obligation, bank issues?','','multi','single','','','1','20',NULL,'3','1','1','0','1','2021-06-07 11:32:45','2021-06-07 11:32:45'),(1932,92,'Can banks grant term loans in foreign currency?','','multi','single','','','1','20',NULL,'1','1','1','0','1','2021-06-07 11:33:49','2021-06-07 11:33:49'),(1933,92,'Banks grants term loans in foreign currency out of?','','multi','single','','','1','20',NULL,'3','1','1','0','1','2021-06-07 11:39:49','2021-06-07 11:39:49'),(1934,92,'ECB framework comprises of how many tracks?','','multi','single','','','1','21',NULL,'3','1','1','0','1','2021-06-07 11:40:58','2021-06-07 11:40:58'),(1935,92,'Commercial loans are raised by_____?','','multi','single','','','1','21',NULL,'1','1','1','0','1','2021-06-07 11:41:49','2021-06-07 11:41:49'),(1936,92,'Which track has  minimum average maturity of 3/5 years(INR)?','','multi','single','','','1','21',NULL,'2','1','1','0','1','2021-06-07 11:42:38','2021-06-07 11:42:38'),(1937,92,'Which track has Medium term - minimum average maturity of 3/5 years. (F.C.)?','','multi','single','','','1','21',NULL,'1','1','1','0','1','2021-06-07 11:43:24','2021-06-07 11:43:24'),(1938,92,'Which track has Long term - minimum average maturity of 10 years. (F.C.)?','','multi','single','','','1','21',NULL,'4','1','1','0','1','2021-06-07 11:44:14','2021-06-07 11:44:14'),(1939,92,'Which of the following comes under ECB?','','multi','single','','','1','22',NULL,'4','1','1','0','1','2021-06-07 11:48:46','2021-06-07 11:48:46'),(1940,92,'Do buyer\'s credit comes under ECB?','','multi','single','','','1','22',NULL,'1','1','1','0','1','2021-06-07 11:49:55','2021-06-07 11:49:55'),(1941,92,'What are the forms of ECB?','','multi','single','','','1','22',NULL,'4','1','1','0','1','2021-06-07 11:50:49','2021-06-07 11:50:49'),(1942,92,'What the parameters for ECB?','','multi','single','','','1','22',NULL,'3','1','1','0','1','2021-06-07 11:51:44','2021-06-07 11:51:44'),(1943,92,'Loan may be granted to constituents against the security of funds held in their ?','','multi','single','','','1','23',NULL,'4','1','1','0','1','2021-06-07 06:47:23','2021-06-07 12:17:23'),(1944,92,'Resident in India may borrow not exceeding?','','multi','single','','','1','23',NULL,'1','1','1','0','1','2021-06-07 06:48:14','2021-06-07 12:18:14'),(1945,92,'Which of the following institution in India may extend loans in foreign currency?','','multi','single','','','1','23',NULL,'3','1','1','0','1','2021-06-07 06:48:57','2021-06-07 12:18:57'),(1946,92,'Indian companies in India may grant loans to employees of their branches outside India for personal purposes under ?','','multi','single','','','1','23',NULL,'2','1','1','0','1','2021-06-07 06:49:45','2021-06-07 12:19:45'),(1947,92,'Indian entity may lend in foreign currency to its__?','','multi','single','','','1','23',NULL,'3','1','1','0','1','2021-06-07 06:50:32','2021-06-07 12:20:32'),(1948,92,'ECGC issues policies to exporters & encourages banks by issuing_____ to share financial losses in the event of failure of exporters to repay debts?','','multi','single','','','1','24',NULL,'3','1','1','0','1','2021-06-07 11:59:12','2021-06-07 11:59:12'),(1949,92,'ECGC is a_____?','','multi','single','','','1','24',NULL,'4','1','1','0','1','2021-06-07 12:00:24','2021-06-07 12:00:24'),(1950,92,'ECGC provides short term exposure based insurance for____?','','multi','single','','','1','24',NULL,'2','1','1','0','1','2021-06-07 12:01:26','2021-06-07 12:01:26'),(1951,92,'ECGC stands for?','','multi','single','','','1','24',NULL,'3','1','1','0','1','2021-06-07 12:02:38','2021-06-07 12:02:38'),(1952,92,'Policies rendered by ECGC are?','','multi','single','','','1','24',NULL,'4','1','1','0','1','2021-06-07 12:03:58','2021-06-07 12:03:58'),(1953,92,'Does ECGC covers letter of credit confirmation?','','multi','single','','','1','24',NULL,'1','1','1','0','1','2021-06-07 12:05:54','2021-06-07 12:05:54'),(1954,92,'INFINET stands for ?','','multi','single','','','1','25',NULL,'1','1','1','0','1','2021-06-07 12:07:07','2021-06-07 12:07:07'),(1955,92,'Issue of demand draft/ banker\'s cheque is done by?','','multi','single','','','1','25',NULL,'3','1','1','0','1','2021-06-07 12:08:00','2021-06-07 12:08:00'),(1956,92,'Which of the following subsidies are provided by the Indian banks?','','multi','single','','','1','25',NULL,'2','1','1','0','1','2021-06-07 12:09:00','2021-06-07 12:09:00'),(1957,92,'Electronic credit transfer & electronic debit transfer are some of the ______provided by Indian banks?','','multi','single','','','1','25',NULL,'1','1','1','0','1','2021-06-07 12:10:05','2021-06-07 12:10:05'),(1958,92,'What is VSAT?','','multi','single','','','1','25',NULL,'1','1','1','0','1','2021-06-07 12:11:37','2021-06-07 12:11:37'),(1959,92,'11 Export working capital financing','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16230487921623048792.mp4','','1','11',NULL,'1','2','1','0','1','2021-06-07 12:23:12','2021-06-07 12:23:12'),(1960,92,'15  “Running account basis”','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16233952411623395241.mp4','','1','15',NULL,'1','2','1','0','1','2021-06-11 07:07:22','2021-06-11 12:37:22'),(1961,92,'16 Pre-shipment stage gets over','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16233975051623397505.mp4','','1','16',NULL,'1','2','1','0','1','2021-06-11 07:45:07','2021-06-11 13:15:07'),(1962,93,'1 INTRODUCTION OF PROGRAMME.','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16230569611623056961.mp4','','1','1',NULL,'1','2','1','0','1','2021-06-07 14:39:21','2021-06-07 14:39:21'),(1963,93,'2 Introduction of instructor','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16230570511623057051.mp4','','1','2',NULL,'1','2','1','0','1','2021-06-28 06:29:17','2021-06-28 11:59:17'),(1964,93,'How to improve your sales performance?','','single','single','','','1','3',NULL,'1','2','1','1','1','2021-06-09 11:20:56','2021-06-09 16:50:56'),(1965,93,'Choose the activity goals that we can control?','','single','single','','','1','3',NULL,'1','1','1','0','1','2021-06-07 14:46:29','2021-06-07 14:46:29'),(1966,93,'What you should emphasize of your product in order to reduce costs and solve problems for the customer?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-07 14:47:58','2021-06-07 14:47:58'),(1967,93,'What are  the keys in creating favourable attention.','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-07 14:52:53','2021-06-07 14:52:53'),(1968,93,'Which three words summarize success in sales?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-07 14:55:22','2021-06-07 14:55:22'),(1969,93,'We should be creative in?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-07 14:57:45','2021-06-07 14:57:45'),(1970,93,'The measurement of sales activity against the goals outlined in your sales plan is the ..............','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-07 15:00:03','2021-06-07 15:00:03'),(1971,93,'What lays out your team objectives, your processes, and strategies, and it defines how you will measure success?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-07 15:02:24','2021-06-07 15:02:24'),(1972,93,'Without what most of us would end up lost?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-07 15:04:04','2021-06-07 15:04:04'),(1973,93,'What is the full form of CRM?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-07 15:05:15','2021-06-07 15:05:15'),(1974,93,'What can also make your life easier by automating pieces of the sales process.','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-07 15:06:42','2021-06-07 15:06:42'),(1975,93,'What includes any information or data that helps you to understand prospective and existing customers better before communicating with them?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-07 15:09:33','2021-06-07 15:09:33'),(1976,93,'What occurs when an existing customer is so delighted by the solution that you provide that they feel compelled to recommend you to other prospective customers like themselves?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-07 15:13:16','2021-06-07 15:13:16'),(1977,93,'What is one of the most important criteria buyers use when making a decision, and referrals provide your business?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-07 15:14:29','2021-06-07 15:14:29'),(1978,93,'What is one of the key stages in the sales process?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-07 15:19:16','2021-06-07 15:19:16'),(1979,93,'Who have the opportunity to help people to perform even better by the way you encourage and challenge them as individuals and as a team?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-07 15:21:29','2021-06-07 15:21:29'),(1980,94,'1: INTRODUCTION OF PROGRAMME','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231498721623149872.mp4','','1','1',NULL,'1','2','1','0','1','2021-06-08 16:27:53','2021-06-08 16:27:53'),(1981,94,'2 INTRODUCTION OF INSTRUCTOR','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231499451623149945.mp4','','1','2',NULL,'1','2','1','0','1','2021-06-28 06:30:06','2021-06-28 12:00:06'),(1982,94,'3 OPERATIONS UNDER DOCUMENTARY CREDITS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231505801623150580.mp4','','1','3',NULL,'1','2','1','0','1','2021-06-08 16:39:40','2021-06-08 16:39:40'),(1983,94,'4 PRINCIPLES','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231506941623150694.mp4','','1','4',NULL,'1','2','1','0','1','2021-06-08 16:41:35','2021-06-08 16:41:35'),(1984,94,'5 DEFINITION OF LETTER OF CREDIT','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231513821623151382.mp4','','1','5',NULL,'1','2','1','0','1','2021-06-08 16:53:03','2021-06-08 16:53:03'),(1985,94,'6 OPERATIONS UNDER DOCUMENTARY CREDITS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231514941623151494.mp4','','1','6',NULL,'1','2','1','0','1','2021-06-08 16:54:55','2021-06-08 16:54:55'),(1986,94,'7 UCPDC','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231516281623151628.mp4','','1','7',NULL,'1','2','1','0','1','2021-06-08 16:57:08','2021-06-08 16:57:08'),(1987,94,'10: DISCREPANT DOCUMENTS, WAIVER AND NOTICE','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231518481623151848.mp4','','1','10',NULL,'1','2','1','0','1','2021-06-08 17:00:50','2021-06-08 17:00:50'),(1988,94,'8 CONTENTS OF LC','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231520071623152007.mp4','','1','8',NULL,'1','2','1','0','1','2021-06-08 17:03:28','2021-06-08 17:03:28'),(1989,94,'9 46 A DOCUMENTS REQUIRED','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231552621623155262.mp4','','1','9',NULL,'1','2','1','0','1','2021-06-08 17:57:43','2021-06-08 17:57:43'),(1990,91,'3. Why customers are important?','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16231744061623174406.mp4','','1','3',NULL,'1','2','1','0','1','2021-06-08 23:16:50','2021-06-08 23:16:50'),(1991,94,'_______play a important role to boost the international trade?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-09 09:28:24','2021-06-09 09:28:24'),(1992,94,'What are the principles of the LC?','','multi','single','','','1','4',NULL,'4','1','1','0','1','2021-06-09 09:30:04','2021-06-09 09:30:04'),(1993,94,'LC is in which form?','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-09 09:32:45','2021-06-09 09:32:45'),(1994,94,'LC is issued by?','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-09 09:33:48','2021-06-09 09:33:48'),(1995,94,'Who is considered as an applicant under LC?','','multi','single','','','1','5',NULL,'4','1','1','0','1','2021-06-24 04:57:10','2021-06-24 10:27:10'),(1996,94,'Who is considered as a beneficiary under LC?','','multi','single','','','1','5',NULL,'3','1','1','0','1','2021-06-09 09:36:10','2021-06-09 09:36:10'),(1997,94,'The condition under LC to make payment is within_____?','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-09 09:37:14','2021-06-09 09:37:14'),(1998,94,'With the establishment of LC the buyer is known as?','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-09 09:38:33','2021-06-09 09:38:33'),(1999,94,'With the establishment of LC the seller is known as?','','multi','single','','','1','6',NULL,'3','1','1','0','1','2021-06-09 09:40:26','2021-06-09 09:40:26'),(2000,94,'Under LC the opening bank undertakes contractual obligation and make payment to the?','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-09 09:41:49','2021-06-09 09:41:49'),(2001,94,'Under LC transaction bank deals with the____?','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-09 09:43:49','2021-06-09 09:43:49'),(2002,94,'Do LC protect the buyer from the fraud on the part of an unscrupulous seller?','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-09 09:45:04','2021-06-09 09:45:04'),(2003,94,'Application of______in LC assists parties to have proper understanding and application of terms and condition under LC?','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-09 09:46:10','2021-06-09 09:46:10'),(2004,94,'What does UCPDC stand for?','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-24 05:20:56','2021-06-24 10:50:56'),(2005,94,'What does 600 in UCPDC defines?','','multi','single','','','1','7',NULL,'3','1','1','0','1','2021-06-09 09:48:27','2021-06-09 09:48:27'),(2006,94,'How many articles does UCP 600 has ?','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-09 09:49:34','2021-06-09 09:49:34'),(2007,94,'UCP 600 is effective from which year?','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-09 09:50:30','2021-06-09 09:50:30'),(2008,94,'Set of rules for LC is established by?','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-09 09:51:23','2021-06-09 09:51:23'),(2009,94,'When was the UCP rules first introduced?','','multi','single','','','1','7',NULL,'3','1','1','0','1','2021-06-09 09:52:13','2021-06-09 09:52:13'),(2010,94,'UCP 600 v2.0 is effective from?','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-09 09:53:04','2021-06-09 09:53:04'),(2011,94,'International standard banking practices (ISBP) is in force since?','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-09 09:53:54','2021-06-09 09:53:54'),(2012,94,'Do the UCP 600 provisions supersede the national laws and regulation?','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-09 09:54:49','2021-06-09 09:54:49'),(2013,94,'What does swift stand for?','','multi','single','','','1','7',NULL,'3','1','1','0','1','2021-06-24 05:21:51','2021-06-24 10:51:51'),(2014,94,'Banks in India should not open LC bearing_______clause?','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-09 09:57:00','2021-06-09 09:57:00'),(2015,94,'In the event where nothing is mentioned, the LC is considered to be____?','','multi','single','','','1','8',NULL,'3','1','1','0','1','2021-06-09 05:19:53','2021-06-09 10:49:53'),(2016,94,'Bank with which credit is available or any bank in case of a credit available with any bank?','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-09 05:21:46','2021-06-09 10:51:46'),(2017,94,'What is sight payment?','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-09 05:26:10','2021-06-09 10:56:10'),(2018,94,'Nominated bank makes payment on______?','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-09 05:25:50','2021-06-09 10:55:50'),(2019,94,'Payment made after a specified period of time is called?','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-09 05:23:08','2021-06-09 10:53:08'),(2020,94,'What is the full form of BIC?','','multi','single','','','1','8',NULL,'3','1','1','0','1','2021-06-09 05:27:16','2021-06-09 10:57:16'),(2021,94,'Tenor of the draft should be______from the bill of landing date?','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-09 05:27:53','2021-06-09 10:57:53'),(2022,94,'Under which condition partial shipments are not considered?','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-09 05:28:45','2021-06-09 10:58:45'),(2023,94,'Unloading from one vessel and reloading to another vessel during carriage from port of loading, to the port of discharge stated in credit is called?','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-09 05:29:41','2021-06-09 10:59:41'),(2024,94,'Shipping terms are defined in the______?','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-24 05:39:02','2021-06-24 11:09:02'),(2025,94,'Under which situation the partial shipment is considered?','','multi','single','','','1','8',NULL,'3','1','1','0','1','2021-06-09 05:32:27','2021-06-09 11:02:27'),(2026,94,'Quantity not to exceed or reduce by_____?','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-09 05:33:21','2021-06-09 11:03:21'),(2027,94,'Which of the following are the documents which are required under LC?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-09 04:50:19','2021-06-09 10:20:19'),(2028,94,'Which of the following documents come under commercial documents?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-09 10:19:22','2021-06-09 10:19:22'),(2029,94,'Which of the following are the risk covering documents?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-09 10:21:20','2021-06-09 10:21:20'),(2030,94,'Certificate of origin is a document which comes under?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-09 10:23:07','2021-06-09 10:23:07'),(2031,94,'Export declaration forms and export certificate are which type of document?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-09 10:24:34','2021-06-09 10:24:34'),(2032,94,'IF the LC is silent, then the documents are issued in?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-09 10:26:20','2021-06-09 10:26:20'),(2033,94,'Certificate of origin is issued by_____?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-09 10:28:44','2021-06-09 10:28:44'),(2034,94,'What does GSP mean?','','multi','single','','','1','9',NULL,'4','1','1','0','1','2021-06-24 05:46:22','2021-06-24 11:16:22'),(2035,94,'GSTP has how many member countries?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-09 10:31:47','2021-06-09 10:31:47'),(2036,94,'India has exchanged tariff concessions with_____countries?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-24 05:45:35','2021-06-24 11:15:35'),(2037,94,'Which of the following country is not a part of SAARC?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-09 10:34:30','2021-06-09 10:34:30'),(2038,94,'Under FTA certificate of origin is issued by?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-09 10:36:05','2021-06-09 10:36:05'),(2039,94,'Class certificate is approved by?','','multi','single','','','1','9',NULL,'2','1','1','0','1','2021-06-09 10:37:47','2021-06-09 10:37:47'),(2040,94,'Institute of war clause and institute strike clause with claims payable in_______?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-09 10:42:12','2021-06-09 10:42:12'),(2041,94,'When bank determines that the presentation is not complying it may_______?','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-09 10:43:18','2021-06-09 10:43:18'),(2042,94,'The notice that the bank serves, what does it state?','','multi','single','','','1','10',NULL,'4','1','1','0','1','2021-06-09 10:44:10','2021-06-09 10:44:10'),(2043,94,'Credit can be amended or cancelled with the consent of?','','multi','single','','','1','10',NULL,'3','1','1','0','1','2021-06-09 10:45:05','2021-06-09 10:45:05'),(2044,94,'Partial acceptance of amendment is allowed or not?','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-09 10:45:59','2021-06-09 10:45:59'),(2045,94,'Issuing bank is_____bound by amendment as of time it issues.','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-09 10:47:08','2021-06-09 10:47:08'),(2046,93,'3 How to improve your sales performance?','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232375831623237583.mp4','','1','3',NULL,'1','2','1','0','1','2021-06-09 11:20:24','2021-06-09 16:50:24'),(2047,95,'1 INTRODUCTION OF PROGRAMME','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232356751623235675.mp4','','1','1',NULL,'1','2','1','0','1','2021-06-09 16:17:56','2021-06-09 16:17:56'),(2048,95,'2 INTRODUCTION OF INSTRUCTOR','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232357191623235719.mp4','','1','2',NULL,'1','2','1','0','1','2021-06-28 06:29:36','2021-06-28 11:59:36'),(2049,95,'3 APPLICABLE LAWS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232357641623235764.mp4','','1','3',NULL,'1','2','1','0','1','2021-06-09 16:19:24','2021-06-09 16:19:24'),(2050,95,'4 CONSIGNMENT','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232359421623235942.mp4','','1','4',NULL,'1','2','1','0','1','2021-06-09 16:22:23','2021-06-09 16:22:23'),(2051,95,'5 INGRIDIENTS OF A VALID CONTRACT','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232361111623236111.mp4','','1','5',NULL,'1','2','1','0','1','2021-06-09 16:25:13','2021-06-09 16:25:13'),(2052,95,'6 PRO-FORMA INVOICE','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232362031623236203.mp4','','1','6',NULL,'1','2','1','0','1','2021-06-09 16:26:44','2021-06-09 16:26:44'),(2053,95,'7 SALE PURCHASE CONTRACT','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232362731623236273.mp4','','1','7',NULL,'1','2','1','0','1','2021-06-09 16:27:54','2021-06-09 16:27:54'),(2054,95,'8 WEIGHTS AND MEASURES','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232369821623236982.mp4','','1','8',NULL,'1','2','1','0','1','2021-06-09 16:39:43','2021-06-09 16:39:43'),(2055,95,'9 UNIT PRICE','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232370331623237033.mp4','','1','9',NULL,'1','2','1','0','1','2021-06-09 16:40:34','2021-06-09 16:40:34'),(2056,95,'10 TERMS OF PAYMENT','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232370781623237078.mp4','','1','10',NULL,'1','2','1','0','1','2021-06-09 16:41:19','2021-06-09 16:41:19'),(2057,95,'11 PRICE ESCALATION CLAUSE','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232371141623237114.mp4','','1','11',NULL,'1','2','1','0','1','2021-06-09 16:41:55','2021-06-09 16:41:55'),(2058,95,'12 INSTALLATION & COMMISSIONING.','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232371541623237154.mp4','','1','12',NULL,'1','2','1','0','1','2021-06-09 16:42:35','2021-06-09 16:42:35'),(2059,95,'13 DOCUMENTARY REQUIREMENTS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232371951623237195.mp4','','1','13',NULL,'1','2','1','0','1','2021-06-09 16:43:15','2021-06-09 16:43:15'),(2060,95,'14 SPECIFICATIONS, CANCELLATION CLAIM CLAUSE (should it be claim/claims)','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232372431623237243.mp4','','1','14',NULL,'1','2','1','0','1','2021-06-09 16:44:04','2021-06-09 16:44:04'),(2061,95,'15 FORCE MAJEURE','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232372921623237292.mp4','','1','15',NULL,'1','2','1','0','1','2021-06-09 16:44:53','2021-06-09 16:44:53'),(2062,95,'16 COMPLIANCE WITH LAWS','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16232373361623237336.mp4','','1','16',NULL,'1','2','1','0','1','2021-06-09 16:45:36','2021-06-09 16:45:36'),(2063,95,'17 BREACH OF 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?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-22 08:20:58','2021-06-22 13:50:58'),(2068,95,'What does UNCITRAL stand for in reference to International Contracts ?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-22 08:30:28','2021-06-22 14:00:28'),(2069,95,'When was Indian Carriage of Goods by Sea Act enacted ?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-10 10:47:08','2021-06-10 10:47:08'),(2070,95,'When did the Parliament passed the Bill in terms of the Arbitration and Conciliation Act  ?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-10 10:48:04','2021-06-10 10:48:04'),(2071,95,'Party who appoints the Selling Agent is called ?','','multi','single','','','1','4',NULL,'3','1','1','0','1','2021-06-10 10:50:24','2021-06-10 10:50:24'),(2072,95,'When was INDIAN CONTRACT ACT passed ?','','multi','single','','','1','4',NULL,'2','1','1','0','1','2021-06-10 10:51:18','2021-06-10 10:51:18'),(2073,95,'Goods remain under a TRUST in possession of a Receiving Agent.','','multi','single','','','1','4',NULL,'2','1','1','0','1','2021-06-10 10:52:19','2021-06-10 10:52:19'),(2074,95,'According to INDIAN CONTRACT ACT contract should be in which form ?','','multi','single','','','1','4',NULL,'3','1','1','0','1','2021-06-10 10:53:25','2021-06-10 10:53:25'),(2075,95,'Which form is considered legal ?','','multi','single','','','1','4',NULL,'1','1','1','0','1','2021-06-10 10:54:21','2021-06-10 10:54:21'),(2076,95,'Payment terms under contract may prescribe -','','multi','single','','','1','4',NULL,'4','1','1','0','1','2021-06-10 10:55:30','2021-06-10 10:55:30'),(2077,95,'Sale transaction within India is governed under _________ .','','multi','single','','','1','4',NULL,'4','1','1','0','1','2021-06-10 10:56:52','2021-06-10 10:56:52'),(2078,95,'________ means assent to same terms.','','multi','single','','','1','4',NULL,'3','1','1','0','1','2021-06-10 10:57:51','2021-06-10 10:57:51'),(2079,95,'Contract from Buyer\'s point of view is called as ?','','multi','single','','','1','4',NULL,'2','1','1','0','1','2021-06-10 10:59:03','2021-06-10 10:59:03'),(2080,95,'Contract must include series of Documents.','','multi','single','','','1','4',NULL,'2','1','1','0','1','2021-06-10 10:59:58','2021-06-10 10:59:58'),(2081,95,'Draft Contract can\'t be revised once formulated.','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-22 09:53:10','2021-06-22 15:23:10'),(2082,95,'Pro-Forma Invoice is an __________.','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-10 13:20:32','2021-06-10 13:20:32'),(2083,95,'The language used to draft a Contract should be ?','','multi','single','','','1','5',NULL,'4','1','1','0','1','2021-06-10 13:21:24','2021-06-10 13:21:24'),(2084,95,'Documents should show Terms and Conditions of Sale','','multi','single','','','1','5',NULL,'1','1','1','0','1','2021-06-10 13:22:08','2021-06-10 13:22:08'),(2085,95,'What among the following comes under Ingredients of Valid Contract.','','multi','single','','','1','5',NULL,'4','1','1','0','1','2021-06-10 13:23:01','2021-06-10 13:23:01'),(2086,95,'______ can be converted into ________by advice of Proposer.','','multi','single','','','1','5',NULL,'2','1','1','0','1','2021-06-10 13:24:41','2021-06-10 13:24:41'),(2087,95,'Purchase Department invites market quotations when it has the list of approved suppliers.','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-22 09:56:28','2021-06-22 15:26:28'),(2088,95,'Pro-Forma Invoice is provided to ______ by ___________.','','multi','single','','','1','6',NULL,'1','1','1','0','1','2021-06-10 13:26:28','2021-06-10 13:26:28'),(2089,95,'Who among the following is benefited by the Pro-Forma Invoice to compare prices etc. From different Suppliers.','','multi','single','','','1','6',NULL,'2','1','1','0','1','2021-06-10 13:27:16','2021-06-10 13:27:16'),(2090,95,'Purpose of Contract and nature of Transaction is included in -','','multi','single','','','1','7',NULL,'3','1','1','0','1','2021-06-10 13:28:23','2021-06-10 13:28:23'),(2091,95,'Use of definitions in contract depends on the nature of Contract.','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-10 13:29:09','2021-06-10 13:29:09'),(2092,95,'A Consideration may be a _______  consideration.','','multi','single','','','1','7',NULL,'4','1','1','0','1','2021-06-10 13:30:05','2021-06-10 13:30:05'),(2093,95,'Explained and technical definitions of the Goods should be described.','','multi','single','','','1','7',NULL,'2','1','1','0','1','2021-06-10 13:30:40','2021-06-10 13:30:40'),(2094,95,'Contracts without Considerations are void.','','multi','single','','','1','7',NULL,'1','1','1','0','1','2021-06-22 10:26:13','2021-06-22 15:56:13'),(2095,95,'English Ton is of ______ Pounds.','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-10 13:32:26','2021-06-10 13:32:26'),(2096,95,'Ton may refer to _____.','','multi','single','','','1','8',NULL,'1','1','1','0','1','2021-06-10 13:33:20','2021-06-10 13:33:20'),(2097,95,'USA 100 weight = _________ .','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-10 13:34:17','2021-06-10 13:34:17'),(2098,95,'In India, US Dollar is the currency which can be used for transactions.','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-22 10:29:46','2021-06-22 15:59:46'),(2099,95,'Examples of Metric Unit are ?','','multi','single','','','1','8',NULL,'4','1','1','0','1','2021-06-10 13:40:54','2021-06-10 13:40:54'),(2100,95,'2205 Ibs = _______ kgs.','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-10 13:42:08','2021-06-10 13:42:08'),(2101,95,'Most Countries have adopted ______ system for weights and measures ?','','multi','single','','','1','8',NULL,'2','1','1','0','1','2021-06-10 13:43:21','2021-06-10 13:43:21'),(2102,95,'For exports from India currency for Invoicing is _______ and ______?','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-10 13:44:29','2021-06-10 13:44:29'),(2103,95,'ACU stands for ?','','multi','single','','','1','9',NULL,'3','1','1','0','1','2021-06-10 13:45:27','2021-06-10 13:45:27'),(2104,95,'Appropriate Currency should be selected for the Contract.','','multi','single','','','1','9',NULL,'1','1','1','0','1','2021-06-22 10:55:35','2021-06-22 16:25:35'),(2105,95,'All Bank Charges including Confirmation charges are at __________ .','','multi','single','','','1','10',NULL,'3','1','1','0','1','2021-06-10 13:47:21','2021-06-10 13:47:21'),(2106,95,'_______ may result into late supply of Goods.','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-10 13:48:17','2021-06-10 13:48:17'),(2107,95,'Delivery terms define which of the following ?','','multi','single','','','1','10',NULL,'4','1','1','0','1','2021-06-10 13:49:21','2021-06-10 13:49:21'),(2108,95,'Late presentation of documents may result into pilferage of insurance claim.','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-10 13:50:05','2021-06-10 13:50:05'),(2109,95,'\"STALE DOCUMENTS\" means -','','multi','single','','','1','10',NULL,'2','1','1','0','1','2021-06-10 13:51:09','2021-06-10 13:51:09'),(2110,95,'Method of payment is an essential part of Purchase Contract.','','multi','single','','','1','10',NULL,'1','1','1','0','1','2021-06-10 13:51:52','2021-06-10 13:51:52'),(2111,95,'Price quoted should be fixed for______period of time?','','multi','single','','','1','11',NULL,'3','1','1','0','1','2021-06-10 13:53:00','2021-06-10 13:53:00'),(2112,95,'According to price escalation clause only one price escalation shall be allowed within______?','','multi','single','','','1','11',NULL,'2','1','1','0','1','2021-06-10 13:53:58','2021-06-10 13:53:58'),(2113,95,'Inspection of imported goods can be done by?','','multi','single','','','1','11',NULL,'4','1','1','0','1','2021-06-10 13:55:47','2021-06-10 13:55:47'),(2114,95,'If the buyer require seller\'s engineers or technician who bear their transportation or lodging expenses?','','multi','single','','','1','12',NULL,'1','1','1','0','1','2021-06-10 13:56:54','2021-06-10 13:56:54'),(2115,95,'Visa / entry permit to the technician of the seller is provided by?','','multi','single','','','1','12',NULL,'2','1','1','0','1','2021-06-10 13:57:53','2021-06-10 13:57:53'),(2116,95,'Which of the following work is carried out by buyer sight by the buyers at their cost?','','multi','single','','','1','12',NULL,'4','1','1','0','1','2021-06-10 13:58:59','2021-06-10 13:58:59'),(2117,95,'The insurance documents which are required are?','','multi','single','','','1','13',NULL,'3','1','1','0','1','2021-06-10 14:00:02','2021-06-10 14:00:02'),(2118,95,'Documents which are required In framing of international trade are?','','multi','single','','','1','13',NULL,'4','1','1','0','1','2021-06-10 14:01:00','2021-06-10 14:01:00'),(2119,95,'What does force majeure means?','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-10 14:02:25','2021-06-10 14:02:25'),(2120,95,'What is the point which the affected party needs to prove under force majeure?','','multi','single','','','1','15',NULL,'4','1','1','0','1','2021-06-10 14:03:24','2021-06-10 14:03:24'),(2121,95,'What is literal meaning of force majeure?','','multi','single','','','1','15',NULL,'3','1','1','0','1','2021-06-10 14:04:18','2021-06-10 14:04:18'),(2122,95,'Who has the authority to make a decision as to declare whether an event of force majeure?','','multi','single','','','1','15',NULL,'1','1','1','0','1','2021-06-10 14:05:22','2021-06-10 14:05:22'),(2123,95,'Notice shall be given within____after party became aware of relevant event or circumstances constituting force majeure?','','multi','single','','','1','15',NULL,'2','1','1','0','1','2021-06-10 14:06:18','2021-06-10 14:06:18'),(2124,95,'What is ADR mechanism?','','multi','single','','','1','16',NULL,'3','1','1','0','1','2021-06-10 14:07:33','2021-06-10 14:07:33'),(2125,95,'Any dispute arising during execution of contract shall be referred to which arbitration?','','multi','single','','','1','16',NULL,'2','1','1','0','1','2021-06-10 14:08:33','2021-06-10 14:08:33'),(2126,95,'The seat and venue of arbitration shall be?','','multi','single','','','1','16',NULL,'1','1','1','0','1','2021-06-10 14:09:29','2021-06-10 14:09:29'),(2127,95,'The language of the arbitration shall be?','','multi','single','','','1','16',NULL,'4','1','1','0','1','2021-06-10 14:10:21','2021-06-10 14:10:21'),(2128,95,'Contract should take care of factors like?','','multi','single','','','1','16',NULL,'3','1','1','0','1','2021-06-10 14:11:13','2021-06-10 14:11:13'),(2129,95,'All dustout arising out of or in connection with the present contract shall be finally settled under rules of arbitration of the_______?','','multi','single','','','1','16',NULL,'2','1','1','0','1','2021-06-10 14:12:37','2021-06-10 14:12:37'),(2130,95,'In the event of the breach of the contract the aggrieved party may be compensated by the_______?','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-10 14:14:03','2021-06-10 14:14:03'),(2131,95,'Damages are of_____types?','','multi','single','','','1','17',NULL,'2','1','1','0','1','2021-06-10 14:15:22','2021-06-10 14:15:22'),(2132,95,'Which of the following is one of the type of damage?','','multi','single','','','1','17',NULL,'3','1','1','0','1','2021-06-10 14:16:13','2021-06-10 14:16:13'),(2133,95,'What does Rescission means?','','multi','single','','','1','17',NULL,'4','1','1','0','1','2021-06-10 14:17:14','2021-06-10 14:17:14'),(2134,95,'What does restitution means?','','multi','single','','','1','17',NULL,'2','1','1','0','1','2021-06-10 14:18:10','2021-06-10 14:18:10'),(2135,95,'Equitable remedy that allows party to rewrite/reform contract as originally created?','','multi','single','','','1','17',NULL,'1','1','1','0','1','2021-06-10 14:19:04','2021-06-10 14:19:04'),(2136,95,'_____stipulates predetermined sum of money that must be paid as damages in the event of the failure to perform specified duty under a contract?','','multi','single','','','1','18',NULL,'1','1','1','0','1','2021-06-22 11:30:31','2021-06-22 17:00:31'),(2137,95,'If the party wants to assign the rights and obligation under present contract to a third party, what the party has to do?','','multi','single','','','1','18',NULL,'2','1','1','0','1','2021-06-10 14:22:42','2021-06-10 14:22:42'),(2138,95,'Which of the following are the additional important contract provisions?','','multi','single','','','1','19',NULL,'4','1','1','0','1','2021-06-10 14:24:03','2021-06-10 14:24:03'),(2139,95,'How many types of additional important contract provisions are there?','','multi','single','','','1','19',NULL,'2','1','1','0','1','2021-06-10 14:24:53','2021-06-10 14:24:53'),(2140,95,'Seller is required to acknowledge and confirm acceptance of contract on terms and conditions stipulated within a period of____?','','multi','single','','','1','19',NULL,'3','1','1','0','1','2021-06-10 14:25:45','2021-06-10 14:25:45'),(2141,96,'1 INTRODUCTION OF PROGRAMME','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16233161301623316130.mp4','','1','1',NULL,'1','2','1','0','1','2021-06-10 14:38:51','2021-06-10 14:38:51'),(2142,96,'2 INTRODUCTION OF INSTRUCTOR','','multi','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16233162211623316221.mp4','','1','2',NULL,'1','2','1','0','1','2021-06-28 06:30:22','2021-06-28 12:00:22'),(2143,96,'To whom you are actually selling?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-10 15:01:37','2021-06-10 15:01:37'),(2144,96,'Why potential customers can be bored by you?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-10 15:05:18','2021-06-10 15:05:18'),(2145,96,'A good salesperson is not an ................','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-10 15:07:02','2021-06-10 15:07:02'),(2146,96,'What you should always remember in your questioning techniques?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-10 15:08:43','2021-06-10 15:08:43'),(2147,96,'How can you get connected and develop yourself?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-10 15:10:17','2021-06-10 15:10:17'),(2148,96,'To outline the benefits of the features of the products, what you should use?','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-10 15:16:09','2021-06-10 15:16:09'),(2149,96,'What is the full form of DMU?','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-10 15:18:25','2021-06-10 15:18:25'),(2150,96,'Customers will only buy from you if they','','multi','single','','','1','3',NULL,'4','1','1','0','1','2021-06-10 11:26:19','2021-06-10 16:56:19'),(2151,96,'What is the key to effective selling?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-10 17:06:10','2021-06-10 17:06:10'),(2152,96,'What are the two factors your credibility is dependent on?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-22 12:36:19','2021-06-22 18:06:19'),(2153,96,'What is the building block of relationships?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-10 17:09:53','2021-06-10 17:09:53'),(2154,96,'What is about  advancing the sale and building the relationship in a way that provides understanding and clarity to both the seller and the prospective client?','','multi','single','','','1','3',NULL,'1','1','1','0','1','2021-06-10 17:12:28','2021-06-10 17:12:28'),(2155,96,'Emotion drives ................ percent of all buying decisions.','','multi','single','','','1','3',NULL,'2','1','1','0','1','2021-06-10 17:14:47','2021-06-10 17:14:47'),(2156,96,'What selling is all about?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-10 17:21:03','2021-06-10 17:21:03'),(2157,96,'What a good salesperson should realise about the buyers?','','multi','single','','','1','3',NULL,'3','1','1','0','1','2021-06-10 17:27:21','2021-06-10 17:27:21'),(2158,96,'Principles of selling','','single','single','https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16233266851623326684.mp4','','1','3',NULL,'1','2','1','0','1','2021-06-16 04:35:49','2021-06-16 10:05:49'),(2159,97,'1 Sampling and Data Introduction','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\">You are probably asking yourself the question, &quot;When and where will I use statistics?&quot; If you read any newspaper, watch&nbsp;&nbsp; television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a television news program, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or <em>fact</em>. Statistical methods can help you make the <em>best educated guess</em>.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Since you will undoubtedly be given statistical information at some point in your life, you need to know some techniques for analyzing the information thoughtfully. Think about buying a house or managing a budget. Think about your chosen profession. The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Included in this chapter are the basic ideas and words of probability and statistics. You will soon understand that statistics and probability work together. You will also learn how data are gathered and what <em>good </em>data can be distinguished from <em>bad</em>.</span></p>','','1','1',NULL,'1','2','1','0','1','2021-06-19 11:28:58','2021-06-19 16:58:58'),(2160,97,'1.1 Definitions of Statistics','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The science of </span><strong><span style=\"color:black\">statistics </span></strong><span style=\"color:black\">deals with the collection, analysis, interpretation, and presentation of </span><strong><span style=\"color:black\">data</span></strong><span style=\"color:black\">. We see and use data in our everyday lives.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called <strong>descriptive statistics</strong>. Two ways to summarize data are by graphing and by using numbers, for example, finding an average. After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from <em>good </em>data.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The formal methods are called <strong>inferential statistics</strong>. Statistical inference uses probability to determine how confident we can be that our conclusions are correct.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Effective interpretation of data, or inference, is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Statistical Models</strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Statistics, like all other branches of mathematics, uses </span><strong><span style=\"color:black\">mathematical models </span></strong><span style=\"color:black\">to describe phenomena that occur in the real world. Some mathematical models are deterministic. These models can be used when one value is precisely determined from another value. Examples of deterministic models are the quadratic equations that describe the acceleration of a car from rest or the differential equations that describe the transfer of heat from a stove to a pot. These models are quite accurate and can be used to answer questions and make predictions with a high degree of precision. Space agencies, for example, use deterministic models to predict the exact amount of thrust that a rocket needs to break away from Earth&rsquo;s gravity and achieve orbit.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">However, life is not always precise. While scientists can predict to the minute the time that the sun will rise, they cannot say precisely where a hurricane will make landfall. </span><strong><span style=\"color:black\">Statistical models </span></strong><span style=\"color:black\">can be used to predict life&rsquo;s more uncertain situations. These special forms of mathematical models or functions are based on the idea that one value affects another value. Some statistical models are mathematical functions that are more precise&mdash;one set of values can predict or determine another set of values. Or some statistical models are mathematical functions in which a set of values do not precisely determine other values. Statistical models are very useful because they can describe the probability or likelihood of an event occurring and&nbsp;&nbsp;&nbsp; provide alternative outcomes if the event&nbsp;does not occur. For example, weather forecasts are examples of statistical models. Meteorologists cannot predict tomorrow&rsquo;s weather with certainty. However, they often use statistical models to tell you how likely it is to rain at any given time, and you can prepare yourself based on this probability.</span></span></p>','','1','1.1',NULL,'1','2','1','0','1','2021-06-19 11:30:18','2021-06-19 17:00:18'),(2161,97,'1.1.1 Probability','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:black\">Probability </span></strong><span style=\"color:black\">is a mathematical tool used to study randomness. It deals with the chance of an event occurring. For example, if you toss a </span><strong><span style=\"color:black\">fair </span></strong><span style=\"color:black\">coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is </span><span class=\"math-tex\">\\(\\frac{1}{2}\\)</span>&nbsp;<span style=\"color:black\">or .5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. After reading about the English statistician Karl </span><strong><span style=\"color:black\">Pearson </span></strong><span style=\"color:black\">who tossed a coin 24,000 times with result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction&nbsp;</span><span class=\"math-tex\">\\(\\frac{996}{2000}\\)</span>&nbsp;<span style=\"color:black\">is equal to .498 which is very close to .5, the expected probability.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The theory of probability began with the study of games of chance such as poker. Predictions take the form of probabilities.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">To predict the likelihood of an earthquake, of rain, or whether you will get an </span><em><span style=\"color:black\">A </span></em><span style=\"color:black\">in this course, we use probabilities. Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. A stockbroker uses probability to determine the rate of return on a client&#39;s investments.</span></span></p>','','1','1.1.1',NULL,'1','2','1','0','1','2021-06-19 11:34:07','2021-06-19 17:04:07'),(2162,97,'1.1.2 Key Terms','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">In statistics, we generally want to study a </span><strong><span style=\"color:black\">population</span></strong><span style=\"color:black\">. You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a </span><strong><span style=\"color:black\">sample</span></strong><span style=\"color:black\">. The idea of </span><strong><span style=\"color:black\">sampling </span></strong><span style=\"color:black\">is to select a portion, or subset, of the larger population and study that portion&mdash;the sample&mdash;to gain information about the population. Data are the result of sampling from a population.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students&#39; grade point averages. In presidential elections, opinion poll samples of 1,000&ndash;2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16-ml can contain 16 ml of carbonated drink.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">From the sample data, we can calculate a statistic. A </span><strong><span style=\"color:black\">statistic </span></strong><span style=\"color:black\">is a number that represents a property of the sample. For example, if we consider one math class as a sample of the population of </span><em><span style=\"color:black\">all </span></em><span style=\"color:black\">math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. Since we do not have the data for all math classes, that statistic is our best estimate of the average for the entire population of math classes. If we happen to have data for </span><em><span style=\"color:black\">all </span></em><span style=\"color:black\">math classes, we can find the population parameter. A </span><strong><span style=\"color:black\">parameter </span></strong><span style=\"color:black\">is a numerical characteristic of the whole population that can be estimated by a statistic. Since we&nbsp;considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. In order to have an accurate sample, it must contain the characteristics of the population in order to be a </span><strong><span style=\"color:black\">representative sample</span></strong><span style=\"color:black\">. We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">A </span><strong><span style=\"color:black\">variable</span></strong><span style=\"color:black\">, usually notated by capital letters such as </span><em><span style=\"color:black\">X </span></em><span style=\"color:black\">and </span><em><span style=\"color:black\">Y</span></em><span style=\"color:black\">, is a characteristic or measurement that can be determined for each member of a population. Variables may describe values like weight in pounds or favorite subject in school. </span><strong><span style=\"color:black\">Numerical variables </span></strong><span style=\"color:black\">take on values with equal units such as weight in pounds and time in hours. </span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:black\">Categorical variables </span></strong><span style=\"color:black\">place the person or thing into a category. If we let </span><em><span style=\"color:black\">X </span></em><span style=\"color:black\">equal the number of points earned by one math student at the end of a term, then </span><em><span style=\"color:black\">X </span></em><span style=\"color:black\">is a numerical variable. If we let </span><em><span style=\"color:black\">Y </span></em><span style=\"color:black\">be a person&#39;s party affiliation, then some examples of </span><em><span style=\"color:black\">Y </span></em><span style=\"color:black\">include BJP, INC, AAP, NCP, JD. </span><em><span style=\"color:black\">Y </span></em><span style=\"color:black\">is a categorical variable. </span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">We could do some math with values of </span><em><span style=\"color:black\">X</span></em><span style=\"color:black\">&mdash;calculate the average number of points earned, for example&mdash;but it makes no sense to do math with values of </span><em><span style=\"color:black\">Y</span></em><span style=\"color:black\">&mdash;calculating an average party affiliation makes no sense.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:black\">Data </span></strong><span style=\"color:black\">are the actual values of the variable. They may be numbers or they may be words. </span><strong><span style=\"color:black\">Datum </span></strong><span style=\"color:black\">is a single value.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Two words that come up often in statistics are </span><strong><span style=\"color:black\">mean </span></strong><span style=\"color:black\">and </span><strong><span style=\"color:black\">proportion</span></strong><span style=\"color:black\">. If you were to take three exams in your math classes and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by three. Your mean score would be 84.3 to one decimal place. If, in your math class, there are 40 students and 22 are </span>males and 18 females, then the proportion of men students is <span class=\"math-tex\">\\(\\frac{22}{40}\\)</span>&nbsp;and the proportion of women students is&nbsp;<span class=\"math-tex\">\\(\\frac{18}{40}\\)</span>. Mean and proportion are discussed in more detail in later chapters.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:-1px; text-align:justify\"><span style=\"font-size:14px\"><strong>NOTE:</strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The words </span><em><span style=\"color:black\">mean </span></em><span style=\"color:black\">and </span><em><span style=\"color:black\">average </span></em><span style=\"color:black\">are often used interchangeably. In this book, we use the term </span><em><span style=\"color:black\">arithmetic mean </span></em><span style=\"color:black\">for mean. The substitution of one word for the other is common practice. The technical term is &ldquo;arithmetic mean,&rdquo; and &ldquo;average&rdquo; is technically a center location. However in practice among non-statisticians, &ldquo;average&rdquo; is commonly accepted for &ldquo;arithmetical mean&rdquo;</span></span></p>\n\n<p>&nbsp;</p>','','1','1.1.2',NULL,'1','2','1','0','1','2021-06-19 11:41:15','2021-06-19 17:11:15'),(2163,97,'1.1.3 Examples','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Example 1.1.</strong></span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.</span></span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">We want to know the mean amount of extracurricular activities in which high school students participate. We randomly surveyed 100 high school students. Three of those students were in 2, 5, and 7 extracurricular activities, respectively.</span></span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Solution 1.1</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">population </span></strong><span style=\"color:black\">is all high school students.</span></span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">sample </span></strong><span style=\"color:black\">is the 100 high school students interviewed.</span></span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">parameter </span></strong><span style=\"color:black\">is the mean amount of extracurricular activities in which all high school students participate.</span></span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">statistic </span></strong><span style=\"color:black\">is the mean amount of extracurricular activities in which the sample of high school students&nbsp;participate.</span></span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">variable </span></strong><span style=\"color:black\">could be the amount of extracurricular activities by one high school student. Let </span><em><span style=\"color:black\">X </span></em><span style=\"color:black\">= the amount of&nbsp;extracurricular activities by one high school student. </span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">data </span></strong><span style=\"color:black\">are the number.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Example 1.2</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Determine what the key terms refer to in the following study.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">A study was conducted at a local high school to analyze the average cumulative GPAs of students who graduated</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">last year. </span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Fill in the letter of the phrase that best describes each of the items below.</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">1. Population ____ 2. Statistic ____ 3. Parameter ____ 4. Sample ____ 5. Variable ____ 6. Data ____</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">a) all students who attended the high school last year</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">b) the cumulative GPA of one student who graduated from the high school last year</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">c) 3.65, 2.80, 1.50, 3.90</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">d) a group of students who graduated from the high school last year, randomly selected</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">e) the average cumulative GPA of students who graduated from the high school last year</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">f) all students who graduated from the high school last year</span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\"><span style=\"font-size:14px\">g) the average cumulative GPA of students in the study who graduated from the high school last year</span></p>\n\n<p style=\"margin-left:-2px; text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Solution 1.2</strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">1. f; 2. g; 3. e; 4. d; 5. b; 6. C</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Example 1.3</strong></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.</span></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected and reviewed data about the effects of an automobile crash on test dummies. Here is the criterion they used.</span></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"MsoTableGrid\" style=\"border-collapse:collapse; border:none; height:200px; margin-left:88px; width:1000px\">\n	<caption>\n	<p><span style=\"font-size:18px\"><strong>Table 1.1</strong></span></p>\n	</caption>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:16px; vertical-align:top; width:195px\">\n			<div style=\"text-align:center\"><span style=\"font-size:18px\"><strong><span style=\"color:black\">Speed at which Cars Crashed</span></strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:16px; vertical-align:top; width:243px\">\n			<div style=\"text-align:center\"><span style=\"font-size:18px\"><strong><span style=\"color:black\">Location of </span><em><span style=\"color:black\">Driver </span></em><span style=\"color:black\">(i.e., dummies)</span></strong></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px; vertical-align:top; width:195px\">\n			<div style=\"text-align:center\"><span style=\"font-size:18px\"><span style=\"color:black\">35 miles/hour</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px; vertical-align:top; width:243px\">\n			<div style=\"text-align:center\"><span style=\"font-size:18px\"><span style=\"color:black\">Front seat</span></span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#26397f\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</span></strong></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Cars with dummies in the front seats were crashed into a wall at a speed of 35 miles per hour. We want to know the proportion of dummies in the driver&rsquo;s seat that would have had head injuries, if they had been actual drivers. We start with a simple random sample of 75 cars.</span></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Solution 1.3</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">population </span></strong><span style=\"color:black\">is all cars containing dummies in the front seat.</span></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">sample </span></strong><span style=\"color:black\">is the 75 cars, selected by a simple random sample.</span></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">parameter </span></strong><span style=\"color:black\">is the proportion of driver dummies&mdash;if they had been real people&mdash;who would have suffered head injuries in the population.</span></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">statistic </span></strong><span style=\"color:black\">is proportion of driver dummies&mdash;if they had been real people&mdash;who would have suffered head injuries in the sample.</span></span></p>\n\n<p style=\"margin-left:11px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">variable </span></strong><em><span style=\"color:black\">X </span></em><span style=\"color:black\">= the number of driver dummies&mdash;if they had been real people&mdash;who would have suffered head injuries.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">data </span></strong><span style=\"color:black\">are either: yes, had head injury, or no, did not.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Example 1.4</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:10px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.</span></span></p>\n\n<p style=\"margin-left:10px; text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:10px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit.</span></span></p>\n\n<p style=\"margin-left:10px; text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Solution 1.4</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:10px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">population </span></strong><span style=\"color:black\">is all medical doctors listed in the professional directory.</span></span></p>\n\n<p style=\"margin-left:10px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">parameter </span></strong><span style=\"color:black\">is the proportion of medical doctors who have been involved in one or more malpractice suits in&nbsp;the population.</span></span></p>\n\n<p style=\"margin-left:10px; text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:10px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">sample </span></strong><span style=\"color:black\">is the 500 doctors selected at random from the professional directory.</span></span></p>\n\n<p style=\"margin-left:10px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">statistic </span></strong><span style=\"color:black\">is the proportion of medical doctors who have been involved in one or more malpractice suits in the&nbsp;sample.</span></span></p>\n\n<p style=\"margin-left:9px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><span style=\"color:black\">variable </span></strong><em><span style=\"color:black\">X </span></em><span style=\"color:black\">= the number of medical doctors who have been involved in one or more malpractice suits.</span></span></p>\n\n<p style=\"margin-left:9px; text-align:justify\"><span style=\"font-size:14px\">&nbsp;The <strong>data </strong>are either: yes, was involved in one or more malpractice lawsuits; or no, was not.</span></p>','','1','1.1.3',NULL,'1','2','1','0','1','2021-06-21 06:23:21','2021-06-21 11:53:21'),(2164,97,'1.2 Data','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Data may come from a population or from a sample. Lowercase letters like </span><em><span style=\"color:black\">x </span></em><span style=\"color:black\">or </span><em><span style=\"color:black\">y </span></em><span style=\"color:black\">generally are used to represent data values. Most data can be put into the following categories:</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; Qualitative</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; Quantitative</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:black\">Qualitative data </span></strong><span style=\"color:black\">are the result of categorizing or describing attributes of a population. Qualitative data are also often called </span><strong><span style=\"color:black\">categorical data</span></strong><span style=\"color:black\">. Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. Qualitative data are generally described by words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Blood type might be AB+, O&ndash;, or B+. Researchers often prefer to use quantitative data over qualitative data because it lends itself more easily to mathematical analysis. For example, it does not make sense to find an average hair color or blood type.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:black\">Quantitative data </span></strong><span style=\"color:black\">are always numbers. Quantitative data are the result of </span><strong><span style=\"color:black\">counting </span></strong><span style=\"color:black\">or </span><strong><span style=\"color:black\">measuring </span></strong><span style=\"color:black\">attributes of a population.Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics are examples of quantitative data. Quantitative data may be either </span><strong><span style=\"color:black\">discrete </span></strong><span style=\"color:black\">or </span><strong><span style=\"color:black\">continuous</span></strong><span style=\"color:black\">.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">All data that are the result of counting are called </span><strong><span style=\"color:black\">quantitative discrete data</span></strong><span style=\"color:black\">. These data take on only certain numerical values. If you count the number of phone calls you receive for each day of the week, you might get values such as zero, one, two, or three.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Data that are not only made up of counting numbers, but that may include fractions, decimals, or irrational numbers, are called </span><strong><span style=\"color:black\">quantitative continuous data</span></strong><span style=\"color:black\">. Continuous data are often the results of measurements like lengths, weights, or times.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">A list of the lengths in minutes for all the phone calls that you make in a week, with numbers like 2.4, 7.5, or 11.0, would be quantitative continuous data.</span></span></p>','','1','1.2',NULL,'1','2','1','0','1','2021-06-11 16:46:24','2021-06-11 16:46:24'),(2165,97,'1.2.1 Examlpes','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Example 1.5 Data Sample of Quantitative Discrete Data</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<div>\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The data are the number of books students carry in their backpacks. You sample five students. Two students carry three books, one student carries four books, one student carries two books, and one student carries one book. Thenumbers of books, 3, 4, 2, and 1, are the quantitative discrete data.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Example 1.6 Data Sample of Quantitative Continuous Data</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The data are the weights of backpacks with books in them. You sample the same five students. The weights (in pounds) of their backpacks are 6.2, 7, 6.8, 9.1, 4.3. Notice that backpacks carrying three books can have different weights. Weights are quantitative continuous data.</span></p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;1.7</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<div>\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">You go to the supermarket and purchase three cans of soup (500ml) tomato soup, (200ml) &nbsp;lentil, and (300ml) sweet corn, two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts (750ml) pistachio ice cream and 100gms of chocolate chip cookies).</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Name data sets that are quantitative discrete, quantitative continuous, and qualitative(categorical).</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">One Possible Solution:</span></p>\n\n<p>&nbsp;</p>\n\n<div>\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The three cans of soup, two packages of nuts, four kinds of vegetables and two desserts are quantitative discrete data because you count them.</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The weights of the soups (500ml, 300ml,200 ml) are quantitative continuous data because you measure weights as precisely as possible.</span></p>\n\n<p><span style=\"font-size:14px\">Types of soups, nuts, vegetables and desserts are qualitative(categorical) data because they are categorical.</span></p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAmple 1.8</strong></span></span></p>\n\n<div>\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The data are the colors of backpacks. Again, you sample the same five students. One student has a red backpack, two students have black backpacks, one student has a green backpack, and one student has a gray backpack. The colors <span style=\"color:#424242\">red, black, black, green, and gray are qualitative data.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAmple 1.9</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<div>\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Work collaboratively to determine the correct data type: quantitative or qualitative. Indicate whether quantitative data are continuous or discrete. Hint: Data that are discrete often start with the words the number of.</span></p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">the number of pairs of shoes you own</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">the type of car you drive</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">the distance from your home to the nearest grocery store</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">the number of classes you take per school year</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">the type of calculator you use</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">weights of sumo wrestlers</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">number of correct answers on a quiz</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">IQ scores (This may cause some discussion<span style=\"color:black\">.)</span></span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution 1.9</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Items a, d, and g are quantitative discrete; items c, f, and h are quantitative continuous; items b and e are qualitative or categorical.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;1.10</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<div>\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">A statistics professor collects information about the classification of her medical students as 1<sup>st</sup> year, 2<sup>nd</sup> year , 3<sup>rd</sup> year and 4<sup>th</sup> year. The data she collects are summarized in the pie chart<u><span style=\"color:#027eb5\">.</span></u></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">What type of data does this graph show?</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234104981623410498.jpg\" style=\"height:605px; width:800px\" /></span></p>\n\n<p>&nbsp;</p>\n\n<div>\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;1.10</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">This pie chart shows the students in each year, which is&nbsp;<strong><span style=\"color:#424242\">qualitative (or categorical) data</span></strong>.</span></p>\n</div>\n</div>\n</div>\n</div>\n</div>\n</div>\n</div>','','1','1.2.1',NULL,'1','2','1','0','1','2021-06-21 07:47:47','2021-06-21 13:17:47'),(2166,97,'1.2.2 Qualitative Data Discussion','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Below are tables comparing the number of part-time and full-time students at St. Mary College and St. Paul College 2020 . The tables display counts (frequencies) and percentages or proportions (relative frequencies). The percent columns make comparing the same categories in the colleges easier. Displaying percentages along with the numbers is often helpful, but it is particularly important when comparing sets of data that do not have the same totals, such as the total enrollments for both colleges in this example. Notice how much larger the percentage for part-time students at St. Mary College is compared to St. Paul College.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\" summary=\"Table 1.2 Fall Term 2007 (Census day) \">\n	<thead>\n		<tr>\n			<td colspan=\"3\" style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:16px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>St. Mary College</strong></span></div>\n			</td>\n			<td style=\"border-bottom:none; border-left:none; border-right:1px solid black; border-top:none; height:16px; text-align:justify; vertical-align:bottom\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td colspan=\"3\" style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:16px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>St. Paul College</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:16px; text-align:justify\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Number</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Percent</span></div>\n			</td>\n			<td style=\"border-bottom:none; border-left:none; border-right:1px solid black; border-top:none; height:16px; text-align:justify\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px; text-align:justify\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Number</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Percent</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Full-time</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">9,200</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">40.9%</span></div>\n			</td>\n			<td style=\"border-bottom:none; border-left:none; border-right:1px solid black; border-top:none; height:17px; text-align:justify\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Full-time</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4,059</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">28.6%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Part-time</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">13,296</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">59.1%</span></div>\n			</td>\n			<td style=\"border-bottom:none; border-left:none; border-right:1px solid black; border-top:none; height:16px; text-align:justify\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Part-time</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">10,124</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">71.4%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Total</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">22,496</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">100%</span></div>\n			</td>\n			<td style=\"border-bottom:none; border-left:none; border-right:1px solid black; border-top:none; height:16px; text-align:justify\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Total</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">14,183</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:16px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">100%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:#424242\">Table1.2</span></strong><span style=\"color:#424242\">&nbsp;Term 2020 (Census day)</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Tables are a good way of organizing and displaying data. But graphs can be even more helpful in understanding the data. There are no strict rules concerning which graphs to use. Two graphs that are used to display qualitative(categorical) data are pie charts and bar graphs.</span></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">In a&nbsp;<strong>pie chart</strong>, categories of data are represented by wedges in a circle and are proportional in size to the percent of individuals in each category.</span></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">In a&nbsp;<strong>bar graph</strong>, the length of the bar for each category is proportional to the number or percent of individuals in each category. Bars may be vertical or horizontal.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">A&nbsp;<strong>Pareto chart</strong>&nbsp;consists of bars that are sorted into order by category size (largest to smallest).</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Look at&nbsp;</span><span style=\"color:black\"><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-2-data-sampling-and-variation-in-data-and-sampling#ch01_mod02_fig003\"><span style=\"color:#027eb5\">Figure 1.4</span></a></span><span style=\"color:#424242\">&nbsp;and&nbsp;</span><span style=\"color:black\"><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-2-data-sampling-and-variation-in-data-and-sampling#ch01_mod02_fig004\"><span style=\"color:#027eb5\">Figure 1.5</span></a></span><span style=\"color:#424242\">&nbsp;and determine which graph (pie or bar) you think displays the comparisons better.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">It is a good idea to look at a variety of graphs to see which is the most helpful in displaying the data. We might make different choices of what we think is the &ldquo;best&rdquo; graph depending on the data and the context. Our choice also depends on what we are using the data for.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:center\"><span style=\"font-size:16px\"><strong><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-2-data-sampling-and-variation-in-data-and-sampling#ch01_mod02_fig003\"><span style=\"color:#000000\"><span style=\"background-color:#ffffff\">Figure 1.4</span></span></a></strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\"><span style=\"color:#027eb5\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234110891623411089.jpg\" style=\"height:635px; width:800px\" /></span></span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\"><span style=\"color:#027eb5\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234111221623411122.jpg\" style=\"height:628px; width:800px\" /></span></span></span></span></p>\n\n<p style=\"text-align:center\">&nbsp;</p>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><strong><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-2-data-sampling-and-variation-in-data-and-sampling#ch01_mod02_fig004\"><span style=\"color:#000000\">Figure 1.5</span></a></strong></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#027eb5\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234111571623411157.jpg\" style=\"height:609px; width:800px\" /></span></span></p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><span style=\"background-color:white\">Percentages That Add to More (or Less) Than 100%</span></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Sometimes percentages add up to be more than 100% (or less than 100%). In the graph, the percentages add to more than 100% because students can be in more than one category. A bar graph is appropriate to compare the relative size of the categories. A pie chart cannot be used. It also could not be used if the percentages added to less than 100%.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\" summary=\"Table 1.3 De Anza College Spring 2010 \">\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:24px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Characteristic/category</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:24px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Percent</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Full-time students</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">40.9%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Students who intend to transfer to a 4-year educational institution</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">48.6%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Students under age 25</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">61.0%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">TOTAL</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">150.5%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:#424242\">Table1.3</span></strong><span style=\"color:#424242\">&nbsp;St. Paul College 2020</span></span></span></p>\n\n<p style=\"text-align:center\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234112401623411240.png\" style=\"height:638px; width:800px\" /></span></span></span></p>\n\n<p style=\"text-align:center\"><span style=\"font-size:16px\"><strong><span style=\"background-color:#ffffff\">Figure 1.7</span></strong></span></p>','','1','1.2.2',NULL,'1','2','1','0','1','2021-06-21 07:59:50','2021-06-21 13:29:50'),(2167,97,'1.2.3 Omitting Categories/Missing Data','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">The table displays Ethnicity of Students but is missing the &quot;Other/Unknown&quot; category. This category contains people who did not feel they fit into any of the ethnicity categories or declined to respond. Notice that the frequencies do not add up to the total number of students. In this situation, create a bar graph and not a pie chart.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\" summary=\"Table 1.4 Ethnicity of Students at De Anza College Fall Term 2007 (Census Day) \">\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:30px; vertical-align:bottom\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:30px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\"><strong>Frequency</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:30px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\"><strong>Percent</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">AP</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">8,794</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">36.1%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:30px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">Maharastra</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">1,412</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">5.8%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">Gujarat</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">1,298</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<div style=\"text-align:center\"><span style=\"font-size:24px\">5.3%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:30px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">MP</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">4,180</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">17.1%</span></p>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">Orissa</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">146</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">0.6%</span></p>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:30px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">TN</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">236</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">1.0%</span></p>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">Rajasthan</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">5,978</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">24.5%</span></p>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">TOTAL</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">22,044 out of 24,382</span></p>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px\">\n			<p style=\"text-align:center\"><span style=\"font-size:24px\">90.4% out of 100%</span></p>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:#424242\">Table</span></strong><span style=\"color:#424242\">1.4</span>&nbsp;<span style=\"color:#424242\">Ethnicity of Students at St. Paul college 2021 </span></span></span></p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234744311623474431.jpg\" style=\"height:396px; width:800px\" /></span></p>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:#424242\">Figure&nbsp;1.8</span></strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">The following graph is the same as the previous graph but the &ldquo;Other/Unknown&rdquo; percent (9.6%) has been included. The &ldquo;Other/Unknown&rdquo; category is large compared to some of the other categories (Native American, 0.6%, Pacific Islander 1.0%). This is important to know when we think about what the data are telling us.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">This particular bar graph in&nbsp;</span><span style=\"color:black\">Figure 1.9</span><span style=\"color:#424242\">&nbsp;can be difficult to understand visually. The graph in&nbsp;</span><span style=\"color:black\">Figure 1.10</span><span style=\"color:#424242\">&nbsp;is a Pareto chart. The Pareto chart has the bars sorted from largest to smallest and is easier to read and interpret.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234744601623474460.png\" style=\"height:395px; width:800px\" /></span></p>\n\n<p style=\"text-align:center\"><span style=\"font-size:16px\"><span style=\"color:#000000\"><span style=\"background-color:white\"><strong>Figure 1.9 Bar Graph with Other/Unknown Category</strong></span></span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:#26397f\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234745211623474521.jpg\" style=\"height:351px; width:800px\" /></span></strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:center\"><span style=\"font-size:16px\"><span style=\"color:#000000\"><strong>Figure 1.10 Pareto Chart With Bars Sorted by Siz</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:16px\"><span style=\"color:#000000\"><strong>Pie Charts: No Missing Data</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#002060\">The following pie charts have the </span><em><span style=\"color:#002060\">Other/Unknown </span></em><span style=\"color:#002060\">category included since the percentages must add to 100 </span><span style=\"color:black\">percent. The chart in </span><strong><span style=\"color:#26397f\">Figure 1.11</span></strong><span style=\"color:black\">b is organized by the size of each wedge, which makes it a more visually informative graph than the unsorted, alphabetical graph in </span><strong><span style=\"color:#26397f\">Figure 1.11</span></strong><span style=\"color:black\">a.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234745681623474568.jpg\" style=\"height:280px; width:400px\" />&nbsp; &nbsp;&nbsp;<img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234746031623474603.jpg\" style=\"height:292px; width:400px\" /></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:center\"><span style=\"font-size:16px\"><span style=\"color:#000000\"><strong>Figure 1.11</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:16px\"><span style=\"color:#000000\"><strong>Marginal Distributions in Two-Way Tables</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Below is a </span><em><span style=\"color:black\">two-way table</span></em><span style=\"color:black\">, also called a contingency table, showing the favorite sports for 50 adults: 20 women and 30 men.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234747361623474736.png\" style=\"height:305px; width:800px\" /></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">This is a two-way table because it displays information about two categorical variables, in this case, gender and sports. Data <span style=\"color:black\">of this type (two variable data) are referred to as </span><em><span style=\"color:black\">bivariate data</span></em><span style=\"color:black\">. Because the data represent a count, or tally, of choices, itis a two-way </span><em><span style=\"color:black\">frequency </span></em><span style=\"color:black\">table. The entries in the total row and the total column represent marginal frequencies or </span><em><span style=\"color:black\">marginal&nbsp;</span></em></span><span style=\"font-size:14px\"><em><span style=\"color:black\">distributions</span></em><span style=\"color:black\">. Note&mdash;The term marginal distributions get its name from the fact that the distributions are found in the margins of frequency distribution tables. Marginal distributions may be given as a fraction or decimal: For example, the total for men could be given as .6 or 3/5 since 30 / 50 = .6 = 3 / 5. Marginal distributions require bivariate data and only focus on </span><em><span style=\"color:black\">one </span></em><span style=\"color:black\">of the variables represented in the table. In other words, the reason 20 is a marginal frequency in this two-way tabl &nbsp;it represents the margin or portion of the total population that is women (20/50). The reason 25 is a marginal frequency is because it represents the portion of those sampled who favor football (25/50). Note: The values that make up the body of the table (e.g., 20, 8, 2) are called </span><em><span style=\"color:black\">joint frequencies</span></em><span style=\"color:black\">.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:16px\"><span style=\"color:#000000\"><strong>Conditional Distributions in Two-Way Tables</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The distinction between a marginal distribution and a </span><em><span style=\"color:black\">conditional distribution </span></em><span style=\"color:black\">is that the focus is on only a particular subset of the population (not the entire population). For example, in the table, if we focused only on the subpopulation of women who prefer football, then we could calculate the conditional distributions as shown in the two-way table below.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234747931623474793.png\" style=\"height:272px; width:800px\" /></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">To find the first sub-population of women who prefer football, read the value at the intersection of the Women row and Football column which is 5. Then, divide this by the total population of football players which is 25. So, the subpopulation of football players who are women is 5/25 which is .2. Similarly, to find the subpopulation of women who play football, use the value of 5 which is the number of women who play football. Then, divide this by the total population of women which is 20. So, the subpopulation of women who play football is 5/20 which is .25.</span></p>','','1','1.2.3',NULL,'1','2','1','0','1','2021-06-21 08:11:55','2021-06-21 13:41:55'),(2168,97,'1.2.4 Presenting Data','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\">After deciding which graph best represents your data, you may need to present your statistical data to a class or other group in an oral report or multimedia presentation. When giving an oral presentation, you must be prepared to explain exactly how you collected or calculated the data, as well as why you chose the categories, scales, and types of graphs that you are showing. Although you may have made numerous graphs of your data, be sure to use only those that actually demonstrate the stated intentions of your statistical study. While preparing your presentation, be sure that all colors, text, and scales are visible to the entire audience. Finally, make sure to allow time for your audience to ask questions and be prepared to answer them. </span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong>Example 1.11 </strong></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Suppose the guidance counselors at De Anza and Foothill need to make an oral presentation of the student data presented in Figures 1.5 and 1.6. Under what context should they choose to display the pie graph? When might they choose the bar graph? For each graph, explain which features they should point out and the potential display problems that might exist.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>&nbsp;Solution 1.11</strong> </span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The guidance counselors should use the pie graph if the desired information is the percentage of each school&rsquo;s enrollment. They should use the bar graph if knowing the exact numbers of students and the relative sizes of each category at each school are important points to be made. For the pie graph, they should point out which color represents part-time students and which represents full-time students. They should also be sure that the numbers and colors are visible when displayed. For the bar graph, they should point out the scale and the total numbers for each category, and they should be sure that the numbers, colors, and scale marks are all displayed clearly.</span></p>','','1','1.2.4',NULL,'1','2','1','0','1','2021-06-21 08:14:38','2021-06-21 13:44:38'),(2169,97,'1.2.5 Sampling','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Gathering information about an entire population often costs too much or is virtually impossible. Instead, we use a sample of the population.&nbsp;<strong>A sample should have the same characteristics as the population it is representing.</strong>&nbsp;Most statisticians use various methods of random sampling in an attempt to achieve this goal. This section will describe a few of the most common methods. There are several different methods of&nbsp;<strong>random sampling</strong>. In each form of random sampling, each member of a population initially has an equal chance of being selected for the sample. Each method has pros and cons. The easiest method to describe is called a&nbsp;<strong>simple random sample</strong>. Any group of&nbsp;<em>n</em>&nbsp;individuals is equally likely to be chosen as any other group of&nbsp;<em>n</em>&nbsp;individuals if the simple random sampling technique is used. In other words, each sample of the same size has an equal chance of being selected.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Besides simple random sampling, there are other forms of sampling that involve a chance process for getting the sample.&nbsp;<strong>Other well-known random sampling methods are the stratified sample, the cluster sample, and the systematic sample.</strong></span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">To choose a&nbsp;<strong>stratified sample</strong>, divide the population into groups called strata and then take a&nbsp;<strong>proportionate</strong>&nbsp;number from each stratum. For example, you could stratify (group) your college population by department and then choose a proportionate simple random sample from each stratum (each department) to get a stratified random sample. To choose a simple random sample from each department, number each member of the first department, number each member of the second department, and do the same for the remaining departments. Then use simple random sampling to choose proportionate numbers from the first department and do the same for each of the remaining departments. Those numbers picked from the first department, picked from the second department, and so on represent the members who make up the stratified sample.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">To choose a&nbsp;<strong>cluster sample</strong>, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your college population, the four departments make up the cluster sample. Divide your college faculty by department. The departments are the clusters. Number each department, and then choose four different numbers using simple random sampling. All members of the four departments with those numbers are the cluster sample.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">To choose a&nbsp;<strong>systematic sample</strong>, randomly select a starting point and take every&nbsp;<em>n</em><sup>th</sup>&nbsp;piece of data from a listing of the population. For example, suppose you have to do a phone survey. Your phone book contains 20,000 residence listings. You must choose 400 names for the sample. Number the population 1&ndash;20,000 and then use a simple random sample to pick a number that represents the first name in the sample. Then choose every fiftieth name thereafter until you have a total of 400 names (you might have to go back to the beginning of your phone list). Systematic sampling is frequently chosen because it is a simple method.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">A type of sampling that is non-random is convenience sampling.&nbsp;<strong>Convenience sampling</strong>&nbsp;involves using results that are readily available. For example, a computer software store conducts a marketing study by interviewing potential customers who happen to be in the store browsing through the available software. The results of convenience sampling may be very good in some cases and highly biased (favor certain outcomes) in others.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Sampling data should be done very carefully. Collecting data carelessly can have devastating results. Surveys mailed to households and then returned may be very biased (they may favor a certain group). It is better for the person conducting the survey to select the sample respondents.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#424242\">True random sampling is done&nbsp;<strong>with replacement</strong>. That is, once a member is picked, that member goes back into the population and thus may be chosen more than once. However for practical reasons, in most populations, simple random sampling is done&nbsp;<strong>without replacement</strong>. Surveys are typically done without replacement. That is, a member of the population may be chosen only once. Most samples are taken from large populations and the sample tends to be small in comparison to the population. Since this is the case, sampling without replacement is approximately the same as sampling with replacement because the chance of picking the same individual more than once with replacement is very low.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">In a college population of 10,000 people, suppose you want to pick a sample of 1,000 randomly for a survey.&nbsp;<strong>For any particular sample of 1,000</strong>, if you are sampling&nbsp;<strong>with replacement</strong>,</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ul>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">the chance of picking the first person is 1,000 out of 10,000 (0.1000);</span></span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">the chance of picking a different second person for this sample is 999 out of 10,000 (0.0999);</span></span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">the chance of picking the same person again is 1 out of 10,000 (very low).</span></span></span></p>\n	</li>\n</ul>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">If you are sampling&nbsp;<strong>without replacement</strong>,</span></span></span></p>\n\n<ul>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">the chance of picking the first person for any particular sample is 1000 out of 10,000 (0.1000);</span></span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">the chance of picking a different second person is 999 out of 9,999 (0.0999);</span></span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">you do not replace the first person before picking the next person.</span></span></span></p>\n	</li>\n</ul>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Compare the fractions 999/10,000 and 999/9,999. For accuracy, carry the decimal answers to four decimal places. To four decimal places, these numbers are equivalent (0.0999).</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Sampling without replacement instead of sampling with replacement becomes a mathematical issue only when the population is small. For example, if the population is 25 people, the sample is ten, and you are sampling&nbsp;<strong>with replacement for any particular sample</strong>, then the chance of picking the first person is ten out of 25, and the chance of picking a different second person is nine out of 25 (you replace the first person).</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">If you sample&nbsp;<strong>without replacement</strong>, then the chance of picking the first person is ten out of 25, and then the chance of picking the second person (who is different) is nine out of 24 (you do not replace the first person).</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">Compare the fractions 9/25 and 9/24. To four decimal places, 9/25 = 0.3600 and 9/24 = 0.3750. To four decimal places, these numbers are not equivalent.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">When you analyze data, it is important to be aware of&nbsp;<strong>sampling errors</strong>&nbsp;and nonsampling errors. The actual process of sampling causes sampling errors. For example, the sample may not be large enough. Factors not related to the sampling process cause&nbsp;<strong>nonsampling errors</strong>. A defective counting device can cause a nonsampling error.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">In reality, a sample will never be exactly representative of the population so there will always be some sampling error. As a rule, the larger the sample, the smaller the sampling error.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:#424242\">In statistics,&nbsp;<strong>a sampling bias</strong>&nbsp;is created when a sample is collected from a population and some members of the population are not as likely to be chosen as others (remember, each member of the population should have an equally likely chance of being chosen). When a sampling bias happens, there can be incorrect conclusions drawn about the population that is being studied.</span></span></span></p>\n\n<h4 style=\"text-align:justify\">&nbsp;</h4>\n\n<h4 style=\"text-align:justify\"><strong><span style=\"font-size:14px\"><span style=\"color:#2e74b5\"><em><span style=\"color:#333333\">Critical Evaluation</span></em></span></span></strong></h4>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#424242\">We need to evaluate the statistical studies we read about critically and analyze them before accepting the results of the studies. Common problems to be aware of include</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ul>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Problems with samples: A sample must be representative of the population. A sample that is not representative of the population is biased. Biased samples that are not representative of the population give results that are inaccurate and not valid.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Self-selected samples: Responses only by people who choose to respond, such as call-in surveys, are often unreliable.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Sample size issues: Samples that are too small may be unreliable. Larger samples are better, if possible. In some situations, having small samples is unavoidable and can still be used to draw conclusions. Examples: crash testing cars or medical testing for rare conditions</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Undue influence: &nbsp;collecting data or asking questions in a way that influences the response</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Non-response or refusal of subject to participate: &nbsp;The collected responses may no longer be representative of the population. &nbsp;Often, people with strong positive or negative opinions may answer surveys, which can affect the results.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Causality: A relationship between two variables does not mean that one causes the other to occur. They may be related (correlated) because of their relationship through a different variable.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Self-funded or self-interest studies: A study performed by a person or organization in order to support their claim. Is the study impartial? Read the study carefully to evaluate the work. Do not automatically assume that the study is good, but do not automatically assume the study is bad either. Evaluate it on its merits and the work done.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Misleading use of data: improperly displayed graphs, incomplete data, or lack of context</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Confounding: &nbsp;When the effects of multiple factors on a response cannot be separated. &nbsp;Confounding makes it difficult or impossible to draw valid conclusions about the effect of each factor.</span></span></p>\n	</li>\n</ul>','','1','1.2.5',NULL,'1','2','1','0','1','2021-06-12 10:55:51','2021-06-12 10:55:51'),(2170,97,'1.2.6 Examples','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;1.12</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:8px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">A study is done to determine the average tuition that LDR college undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case?</span></span></p>\n\n<p style=\"margin-left:8px; text-align:justify\">&nbsp;</p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#000000\">A sample of 100 undergraduate LDR college students is taken by organizing the students&rsquo; names by classification (1<sup>st</sup> year, 2<sup>nd</sup> year,3<sup>rd</sup> year or 4<sup>th</sup> year), and then selecting 25 students from each.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#000000\">A random number generator is used to select a student from the alphabetical listing of all undergraduate students in the Fall semester. Starting with that student, every 50th student is chosen until 75 students are included in the sample.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#000000\">A completely random method is used to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#000000\">The 1<sup>st</sup> year, 2<sup>nd</sup> year,3<sup>rd</sup> year or 4<sup>th</sup> year are numbered one, two, three, and four, respectively. A random number generator is used to pick two of those years. All students in those two years are in the sample.</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#000000\">An administrative assistant is asked to stand in front of the library one Wednesday and to ask the first 100 undergraduate students he encounters what they paid for tuition the Fall semester. Those 100 students are the sample.</span></span></p>\n	</li>\n</ol>\n\n<p style=\"margin-left:8px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;1.12</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">a. stratified; b. systematic; c. simple random; d. cluster; e. convenience</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;1.13</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">A soccer coach selects six players from a group of boys aged eight to ten, seven players from a group of boys aged 11 to 12, and three players from a group of boys aged 13 to 14 to form a recreational soccer team.</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">A pollster interviews all human resource personnel in five different high tech companies.</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">A high school educational researcher interviews 50 high school female teachers and 50 high school male teachers.</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">A medical researcher interviews every third cancer patient from a list of cancer patients at a local hospital.</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">A high school counselor uses a computer to generate 50 random numbers and then picks students whose names correspond to the numbers.</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">A student interviews classmates in his algebra class to determine how many pairs of jeans a student owns, on the average.</span></span></p>\n	</li>\n</ol>\n\n<p style=\"margin-left:24px; text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:24px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">&nbsp; &nbsp; </span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">&nbsp;a. stratified; b. cluster; c. stratified; d. systematic; e. simple random; f. convenience</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><span style=\"background-color:white\">If we were to examine two samples representing the same population, even if we used random sampling methods for the samples, they would not be exactly the same. Just as there is variation in data, there is variation in samples. As you become accustomed to sampling, the variability will begin to seem natural.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;1.14</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Suppose ABC College has 10,000 part-time students (the population). We are interested in the average amount of money a part-time student spends on books in the fall term. Asking all 10,000 students is an almost impossible task.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Suppose we take two different samples.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">First, we use convenience sampling and survey ten students from a first term organic chemistry class. Many of these students are taking first term calculus in addition to the organic chemistry class. The amount of money they spend on books is as follows:</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Rs.128;&nbsp;Rs.87;&nbsp;Rs.173;&nbsp;Rs.116;&nbsp;Rs.130;&nbsp;</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Rs.204;&nbsp;Rs.147;&nbsp;Rs.189;&nbsp;Rs.93;&nbsp;Rs.153</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">The second sample is taken using a list of senior citizens who take P.E. classes and taking every fifth senior citizen on the list, for a total of ten senior citizens. They spend:</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Rs.50;&nbsp;Rs.40;&nbsp;Rs.36;&nbsp;Rs.15;&nbsp;Rs.50;&nbsp;</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Rs.100;&nbsp;Rs.40;&nbsp;Rs.53;&nbsp;Rs.22;&nbsp;Rs.22</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">It is unlikely that any student is in both samples.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">a. Do you think that either of these samples is representative of (or is characteristic of) the entire 10,000 part-time student population?</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;1</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">a. No. The first sample probably consists of science-oriented students. Besides the chemistry course, some of them are also taking first-term calculus. Books for these classes tend to be expensive. Most of these students are, more than likely, paying more than the average part-time student for their books. The second sample is a group of senior citizens who are, more than likely, taking courses for health and interest. The amount of money they spend on books is probably much less than the average parttime student. Both samples are biased. Also, in both cases, not all students have a chance to be in either sample.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">b. Since these samples are not representative of the entire population, is it wise to use the results to describe the entire population? </span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;2</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">b. No. For these samples, each member of the population did not have an equally likely chance of being chosen.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Now, suppose we take a third sample. We choose ten different part-time students from the disciplines of chemistry, math, English, psychology, sociology, history, nursing, physical education, art, and early childhood development. (We assume that these are the only disciplines in which part-time students at ABC College are enrolled and that an equal number of part-time students are enrolled in each of the disciplines.) Each student is chosen using simple random sampling. Using a calculator, random numbers are generated and a student from a particular discipline is selected if he or she has a corresponding number. The students spend the following amounts:</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Rs.180;&nbsp;Rs.50;&nbsp;Rs.150;&nbsp;Rs.85;&nbsp;Rs.260;</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Rs.75;&nbsp;Rs.180;&nbsp;Rs.200;&nbsp;Rs.200;&nbsp;Rs.150</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">c. Is the sample biased?</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;3</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">c. The sample is unbiased, but a larger sample would be recommended to increase the likelihood that the sample will be close to representative of the population. However, for a biased sampling technique, even a large sample runs the risk of not being representative of the population.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\">Students often ask if it is &quot;good enough&quot; to take a sample, instead of surveying the entire population. If the survey is done well, the answer is yes.</span></span></p>\n\n<p>&nbsp;</p>','','1','1.2.6',NULL,'1','2','1','0','1','2021-06-21 08:34:55','2021-06-21 14:04:55'),(2171,97,'1.2.7 Variation in Data','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:black\">Variation</span></strong><span style=\"color:black\">&nbsp;is present in any set of data. For example, 16-ml cans of beverage may contain more or less than 16 ml of liquid. In one study, eight 16 ml cans were measured and produced the following amount (in ml) of beverage:</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">15.8;&nbsp;16.1;&nbsp;15.2;&nbsp;14.8;&nbsp;15.8;&nbsp;15.9;&nbsp;16.0;&nbsp;</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">15.5</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Measurements of the amount of beverage in a 16-ml can may vary because different people make the measurements or because the exact amount, 16 ml of liquid, was not put into the cans. Manufacturers regularly run tests to determine if the amount of beverage in a 16-ml can falls within the desired range.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Be aware that as you take data, your data may vary somewhat from the data someone else is taking for the same purpose. This is completely natural. However, if two or more of you are taking the same data and get very different results, it is time for you and the others to reevaluate your data-taking methods and your accuracy</span><span style=\"color:#424242\">.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Variation in Samples</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">It was mentioned previously that two or more&nbsp;<strong>samples</strong>&nbsp;from the same&nbsp;<strong>population</strong>, taken randomly, and having close to the same characteristics of the population will likely be different from each other. Suppose <u><span style=\"color:teal\">Dhruv </span></u>and Jeet both decide to study the average amount of time students at their college sleep each night. <u><span style=\"color:teal\">Dhruv</span></u> and Jeet each take samples of 500 students. Doreen uses systematic sampling and Jeet uses cluster sampling. <u><span style=\"color:teal\">Dhruv </span></u>&#39;s sample will be different from Jeet&#39;s sample. Even if <u><span style=\"color:teal\">Dhruv</span></u> and Jeet used the same sampling method, in all likelihood their samples would be different. Neither would be wrong, however.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Think about what contributes to making Dhruv&rsquo;s and Jeet&rsquo;s samples different.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">If Dhruv<u><span style=\"color:teal\"> </span></u>and Jeet took larger samples (i.e. the number of data values is increased), their sample results (the average amount of time a student sleeps) might be closer to the actual population average. But still, their samples would be, in all likelihood, different from each other. This&nbsp;<strong>variability in samples</strong>&nbsp;cannot be stressed enough.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong><span style=\"color:#2e74b5\"><span style=\"color:black\">Size of a Sample</span></span></strong></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The size of a sample (often called the number of observations, usually given the symbol n) is important. The examples you have seen in this book so far have been small. Samples of only a few hundred observations, or even smaller, are sufficient for many purposes. In polling, samples that are from 1,200 to 1,500 observations are considered large enough and good enough if the survey is random and is well done. Later we will find that even much smaller sample sizes will give very good results. You will learn why when you study confidence intervals.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Be aware that many large samples are biased. For example, call-in surveys are invariably biased, because people choose to respond or not.</span></span></p>','','1','1.2.7',NULL,'1','2','1','0','1','2021-06-21 08:47:47','2021-06-21 14:17:47'),(2172,97,'1.3  Frequency, Frequency Tables, and Levels of Measurement','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">Once you have a set of data, you will need to organize it so that you can analyze how frequently each datum occurs in the set. However, when calculating the frequency, you may need to round your answers so that they are as precise as possible.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong>Answers and Rounding Off</strong></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">A simple way to round off answers is to carry your final answer one more decimal place than was present in the original data. Round off only the final answer. Do not round off any intermediate results, if possible. If it becomes necessary to round off intermediate results, carry them to at least twice as many decimal places as the final answer. Expect that some of your answers will vary from the text due to rounding errors.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">It is not necessary to reduce most fractions in this course. Especially in </span><strong><span style=\"color:#26397f\">Probability Topics</span></strong><span style=\"color:black\">, the chapter on probability, it is more helpful to leave an answer as an unreduced fraction.</span></span></span></p>','','1','1.3',NULL,'1','2','1','0','1','2021-06-21 08:50:14','2021-06-21 14:20:14'),(2173,97,'1.3.1 Levels of Measurement','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The way a set of data is measured is called its&nbsp;<strong>level of measurement</strong>. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level):</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ul>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Nominal scale level</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Ordinal scale level</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Interval scale level</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:#424242\">Ratio scale level</span></span></p>\n	</li>\n</ul>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Data that is measured using a&nbsp;<strong>nominal scale</strong>&nbsp;is&nbsp;<strong>qualitative (categorical)</strong>. Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. Nominal scale data are not ordered. For example, trying to classify people according to their favorite food does not make any sense. Putting pizza first and sushi second is not meaningful</span><span style=\"color:#424242\">.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Smartphone companies are another example of nominal scale data. The data are the names of the companies that make smartphones, but there is no agreed upon order of these brands, even though people may have personal preferences. Nominal scale data cannot be used in calculations.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Data that is measured using an&nbsp;<strong>ordinal scale</strong>&nbsp;is similar to nominal scale data but there is a big difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the United States. The top five national parks in the United States can be ranked from one to five but we cannot measure differences between the data.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Another example of using the ordinal scale is a cruise survey where the responses to questions about the cruise are &ldquo;excellent,&rdquo; &ldquo;good,&rdquo; &ldquo;satisfactory,&rdquo; and &ldquo;unsatisfactory.&rdquo; These responses are ordered from the most desired response to the least desired. But the differences between two pieces of data cannot be measured. Like the nominal scale data, ordinal scale data cannot be used in calculations.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Data that is measured using the&nbsp;<strong>interval scale</strong>&nbsp;is similar to ordinal level data because it has a definite ordering but there is a difference between data. The differences between interval scale data can be measured though the data does not have a starting point.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. In both temperature measurements, 40&deg; is equal to 100&deg; minus 60&deg;. Differences make sense. But 0 degrees does not because, in both scales, 0 is not the absolute lowest temperature. Temperatures like -10&deg; F and -15&deg; C exist and are colder than 0.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Interval level data can be used in calculations, but one type of comparison cannot be done. 80&deg; C is not four times as hot as 20&deg; C (nor is 80&deg; F four times as hot as 20&deg; F). There is no meaning to the ratio of 80 to 20 (or four to one).</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Data that is measured using the&nbsp;<strong>ratio scale</strong>&nbsp;takes care of the ratio problem and gives you the most information. Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated. For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The exams are machine-graded.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The data can be put in order from lowest to highest: 20, 68, 80, 92.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. The smallest score is 0. So 80 is four times 20. The score of 80 is four times better than the score of 20.</span></span></p>','','1','1.3.1',NULL,'1','2','1','0','1','2021-06-21 08:51:18','2021-06-21 14:21:18'),(2174,97,'1.3.2 Frequency','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Twenty students were asked how many hours they worked per day. Their responses, in hours, are as follows:&nbsp;</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">5;&nbsp;6;&nbsp;3;&nbsp;3;&nbsp;2;&nbsp;4;&nbsp;7;&nbsp;5;&nbsp;2;&nbsp;3;&nbsp;5;&nbsp;6;&nbsp;5;&nbsp;</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">4;&nbsp;4;&nbsp;3;&nbsp;5;&nbsp;2;&nbsp;5;&nbsp;3.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id10383738\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Table 1.5</span></a><span style=\"color:black\">&nbsp;lists the different data values in ascending order and their frequencies.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"background:white; border-collapse:collapse; border:none; margin-left:132px; width:900px\" summary=\"Table 1.5 Frequency Table of Student Work Hours \">\n	<caption>\n	<p><span style=\"font-size:14px\">Table1.5&nbsp;Frequency Table of Student Work Hours</span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:61%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong><span style=\"color:#424242\">Data value</span></strong></span></div>\n			</td>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong><span style=\"color:#424242\">Frequency</span></strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:61%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">2</span></span></div>\n			</td>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">3</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:61%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">3</span></span></div>\n			</td>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">5</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:61%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">4</span></span></div>\n			</td>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">3</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:61%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">5</span></span></div>\n			</td>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">6</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:61%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">6</span></span></div>\n			</td>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">2</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:61%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">7</span></span></div>\n			</td>\n			<td style=\"background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:#424242\">1</span></span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">A&nbsp;<strong>frequency</strong>&nbsp;is the number of times a value of the data occurs. According to&nbsp;</span><span style=\"color:black\"><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id10383738\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Table 1.5</span></a></span><span style=\"color:black\">, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">A&nbsp;<strong>relative frequency</strong>&nbsp;is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample&ndash;in this case, 20. Relative frequencies can be written as fractions, percent, or decimals.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234767771623476777.png\" style=\"height:504px; width:800px\" /></span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:black\">Table</span></strong><strong><span style=\"color:black\">1.6</span></strong>&nbsp;<span style=\"color:black\">Frequency Table of Student Work Hours with Relative Frequencies</span></span></span></p>\n\n<p style=\"text-align:center\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The sum of the values in the relative frequency column of&nbsp;</span><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id11177380\" style=\"color:blue; text-decoration:underline\"><span style=\"color:#000000\">Table 1.6</span></a><span style=\"color:#000000\">&nbsp;</span><span style=\"color:black\">&nbsp; is</span><em><span style=\"color:black\">&nbsp;&nbsp;<span class=\"math-tex\">\\(\\frac{20}{20}\\)</span></span></em>&nbsp;<span style=\"background-color:white\"><span style=\"color:black\">or 1.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:black\">Cumulative relative frequency</span></strong><span style=\"color:black\">&nbsp;is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in&nbsp;</span><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id10564302\" style=\"color:blue; text-decoration:underline\"><span style=\"color:#000000\">Table 1.7</span></a><span style=\"color:#0070c0\">.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Table1.7&nbsp;Frequency Table of Student Work Hours with Relative and Cumulative Relative Frequencies</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:26px; vertical-align:bottom; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Data value</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:26px; vertical-align:bottom; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Frequency</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:26px; vertical-align:bottom; width:26%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Relative frequency</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:26px; vertical-align:bottom; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Cumulative relative frequency</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><em><span class=\"math-tex\">\\(\\frac{3}{20}\\)</span></em> or .15</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.15</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><em><span class=\"math-tex\">\\(\\frac{5}{20}\\)</span></em> or 0.25</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.15 + 0.25 = 0.40</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><em><span class=\"math-tex\">\\(\\frac{3}{20}\\)</span></em> or 0.15</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.40 + 0.15 = 0.55</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><em><span class=\"math-tex\">\\(\\frac{6}{20}\\)</span></em>&nbsp;or 0.30</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.55 + 0.30 = 0.85</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><em><span class=\"math-tex\">\\(\\frac{2}{20}\\)</span></em>or 0.10</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.85 + 0.10 = 0.95</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:33px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">7</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:33px; width:17%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:33px; width:26%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><em><span class=\"math-tex\">\\(\\frac{1}{20}\\)</span></em> &nbsp;or 0.05</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:33px; width:38%\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.95 + 0.05 = 1.00</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.</span></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\"><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id9703284\" style=\"color:blue; text-decoration:underline\"><span style=\"color:#027eb5\">Table 1.8</span></a></span>&nbsp;<span style=\"color:black\">represents the heights, in inches, of a sample of 100 male semiprofessional soccer players.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234772001623477200.png\" style=\"height:723px; width:800px\" /></span></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"background-color:white\"><span style=\"color:black\">Table1.8</span>&nbsp;<span style=\"color:black\">Frequency Table of Soccer Player Height</span></span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">The data in this table have been&nbsp;<strong>grouped</strong>&nbsp;into the following intervals:</span></span></span></p>\n\n<ul>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">59.95 to 61.95 inches</span></span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">61.95 to 63.95 inches</span></span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">63.95 to 65.95 inches</span></span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">65.95 to 67.95 inches</span></span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">67.95 to 69.95 inches</span></span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">69.95 to 71.95 inches</span></span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">71.95 to 73.95 inches</span></span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">73.95 to 75.95 inches</span></span></span></p>\n	</li>\n</ul>\n\n<p style=\"text-align:justify\"><br />\n<span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">In this sample, there are&nbsp;<strong>five</strong>&nbsp;players whose heights fall within the interval 59.95&ndash;61.95 inches,&nbsp;<strong>three</strong>&nbsp;players whose heights fall within the interval 61.95&ndash;63.95 inches,&nbsp;<strong>15</strong>&nbsp;players whose heights fall within the interval 63.95&ndash;65.95 inches,&nbsp;<strong>40</strong>&nbsp;players whose heights fall within the interval 65.95&ndash;67.95 inches,&nbsp;<strong>17</strong>&nbsp;players whose heights fall within the interval 67.95&ndash;69.95 inches,&nbsp;<strong>12</strong>&nbsp;players whose heights fall within the interval 69.95&ndash;71.95,&nbsp;<strong>seven</strong>&nbsp;players whose heights fall within the interval 71.95&ndash;73.95, and&nbsp;<strong>one</strong>&nbsp;player whose heights fall within the interval 73.95&ndash;75.95. All heights fall between the endpoints of an interval and not at the endpoints</span><span style=\"color:#424242\">.</span></span></span></p>','','1','1.3.2',NULL,'1','2','1','0','1','2021-06-21 09:01:49','2021-06-21 14:31:49'),(2175,97,'1.3.3 Examples','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Example 1.15</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">From </span><span style=\"color:#26397f\">Table 1.8</span><span style=\"color:black\">, find the percentage of heights that are less than 65.95 inches.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Solution 1.15</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">If you look at the first, second, and third rows, the heights are all less than 65.95 inches. There are 5 + 3 + 15 = 23 players whose heights are less than 65.95 inches. The percentage of heights less than 65.95 inches is then 23/100 or 23 percent. This percentage is the cumulative relative frequency entry in the third row.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;1.16</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">From </span><span style=\"color:#26397f\">Table 1.8</span><span style=\"color:black\">, find the percentage of heights that fall between 61.95 and 65.95 inches.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Solution 1.16</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Add the relative frequencies in the second and third rows: .03 + .15 = .18 or 18 percent</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;1.17</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#424242\">From</span>&nbsp;<a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id9703284\" style=\"color:blue; text-decoration:underline\">Table 1.8</a><span style=\"color:#424242\">, find the percentage of heights that fall between 61.95 and 65.95 inches.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">Solution&nbsp;1.17</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Add the relative frequencies in the second and third rows: 0.03 + 0.15 = 0.18 or 18%.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;1.18</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#424242\">Use the heights of the 100 male semiprofessional soccer players in&nbsp;</span><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id9703284\" style=\"color:blue; text-decoration:underline\">Table 1.8</a>.<span style=\"color:#424242\"> Fill in the blanks and check your answers.</span></span></p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">The percentage of heights that are from 67.95 to 71.95 inches is: ____.</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">The percentage of heights that are from 67.95 to 73.95 inches is: ____.</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">The percentage of heights that are more than 65.95 inches is: ____.</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">The number of players in the sample who are between 61.95 and 71.95 inches tall is: ____.</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">What kind of data are the heights?</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">Describe how you could gather this data (the heights) so that the data are characteristic of all male semiprofessional soccer players.</span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Remember, you&nbsp;count frequencies. To find the relative frequency, divide the frequency by the total number of data values. To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">Solution&nbsp;1.18</span></strong></span></p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">29%</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">36%</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">77%</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">87</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">quantitative continuous</span></span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">get rosters from each team and choose a simple random sample from each</span></span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;1.19</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Nineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows:&nbsp;2;&nbsp;5;&nbsp;7;&nbsp;3;&nbsp;2;&nbsp;10;&nbsp;18;&nbsp;15;&nbsp;20;&nbsp;7;&nbsp;10;&nbsp;</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">18;&nbsp;5;&nbsp;12;&nbsp;13;&nbsp;12;&nbsp;4;&nbsp;5;&nbsp;10.&nbsp;</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#id9833287\" style=\"color:blue; text-decoration:underline\">Table 1.10</a>&nbsp;was produced:</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; width:900px\">\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:28px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Data</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:28px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Frequency</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:28px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Relative frequency</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:28px; vertical-align:bottom; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Cumulative relative frequency</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{3}{19}\\)</span> </span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.1579</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; text-align:center\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{3}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.2105</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; text-align:center\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{3}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.1579</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">7</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; text-align:center\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{2}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.2632</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">10</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; text-align:center\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{3}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.4737</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">12</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; text-align:center; vertical-align:top\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{2}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.7895</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">13</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; text-align:center; vertical-align:top\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{1}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.8421</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">15</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; text-align:center; vertical-align:top\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{1}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:27px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.8948</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">18</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; text-align:center; vertical-align:top\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{1}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; width:94px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.9474</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:28px; text-align:center\">\n			<div><span style=\"font-size:28px\">20</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; text-align:center\">\n			<div><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; text-align:center; vertical-align:top\">\n			<div><span style=\"font-size:28px\"><span class=\"math-tex\">\\(\\frac{1}{19}\\)</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:28px; text-align:center; width:94px\">\n			<div><span style=\"font-size:28px\">1,0000</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#424242\">Table1.10</span></strong>&nbsp;<span style=\"color:#424242\">Frequency of Commuting Distances</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">Is the table correct? If it is not correct, what is wrong?</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections.</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">What fraction of the people surveyed commute five or seven miles?</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)?</span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">Solution&nbsp;1.19</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct.</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read: 0.1052, 0.1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000.</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:black\">519519</span></span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\"><span style=\"color:black\">719719,&nbsp;12191219,&nbsp;719719</span></span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;1.20</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><a href=\"https://openstax.org/books/introductory-business-statistics/pages/1-3-levels-of-measurement#fs-idm52810848\" style=\"color:blue; text-decoration:underline\">Table 1.11</a><span style=\"color:#424242\">&nbsp;contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Year</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Total number of deaths</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2000</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">231</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2001</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">21,357</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2002</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">11,685</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2003</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">33,819</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2004</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">228,802</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2005</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">88,003</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2006</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6,605</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2007</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">712</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2008</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">88,011</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2009</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1,790</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2010</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">320,120</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2011</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">21,953</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2012</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">768</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Total</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">823,856</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#424242\">Table1.11</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Answer the following questions.</span></p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">What is the frequency of deaths measured from 2006 through 2009?</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">What percentage of deaths occurred after 2009?</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">What is the relative frequency of deaths that occurred in 2003 or earlier?</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">What is the percentage of deaths that occurred in 2004?</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">What kind of data are the numbers of deaths?</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers?</span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">Solution&nbsp;1.20</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">97,118 (11.8%)</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">41.6%</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">67,092/823,356 or 0.081 or 8.1 %</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">27.8%</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">Quantitative discrete</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">Quantitative continuous</span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>','','1','1.3.3',NULL,'1','2','1','0','1','2021-06-21 10:21:31','2021-06-21 15:51:31'),(2176,97,'1.4 EXPERIMENTAL DESIGN AND ETHICS','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\">Does aspirin reduce the risk of heart attacks? Is one brand of fertilizer more effective at growing roses than another? Is fatigue as dangerous to a driver as speeding? Questions like these are answered using randomized experiments. In this module, you will learn important aspects of experimental design. Proper study design ensures the production of reliable, accurate data.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The purpose of an experiment is to investigate the relationship between two variables. In an experiment, there is the <strong>explanatory variable </strong>which affects the <strong>response variable</strong>. In a randomized experiment, the researcher manipulates the explanatory variable and then observes the response variable. Each value of the explanatory variable used in an experiment is called a <strong>treatment</strong>.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">You want to investigate the effectiveness of vitamin E in preventing disease. You recruit a group of subjects and ask them if they regularly take vitamin E. You notice that the subjects who take vitamin E exhibit better health on average than those who do not. Does this prove that vitamin E is effective in disease prevention? It does not. There are many differences between the two groups compared in addition to vitamin E consumption. People who take vitamin E regularly often take other steps to improve their health: exercise, diet, other vitamin supplements. Any one of these factors could be influencing health. As described, this study does not prove that vitamin E is the key to disease prevention.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Additional variables that can cloud a study are called <strong>lurking variables</strong>. In order to prove that the explanatory variable is causing a change in the response variable, it is necessary to isolate the explanatory variable. The researcher must design her experiment in such a way that there is only one difference between groups being compared: the planned treatments. This is accomplished by the <strong>random assignment </strong>of experimental units to treatment groups. When subjects are assigned treatments <span style=\"color:#424242\">called&nbsp;<strong>treatments</strong>. An&nbsp;<strong>experimental unit</strong>&nbsp;is a single object or individual to be measured.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">The power of suggestion can have an important influence on the outcome of an experiment. Studies have shown that the expectation of the study participant can be as important as the actual medication. In one study of performance-enhancing drugs, researchers noted:</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Randomly, all of the potential lurking variables are spread equally among the groups. At this point the only difference between groups is the one imposed by the researcher. Different outcomes measured in the response variable, therefore, must be a direct result of the different treatments. In this way, an experiment can prove a cause-and-effect connection between the explanatory and response variables.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Confounding occurs when the effects of multiple factors on a response cannot be separated, for instance, if a student guesses on the even-numbered questions on an exam and sits in a favorite spot on exam day. Why does the student get a high test scores on the exam? It could be the increased study time or sitting in the favorite spot or both. Confounding makes it difficult to draw valid conclusions about the effect of each factor on the outcome. The way around this is to test several outcomes with one method (treatment). This way, we know which treatment really works. The power of suggestion can have an important influence on the outcome of an experiment. Studies have shown that the expectation of the study participant can be as important as the actual medication. In one study of performance-enhancing substances, researchers noted the following:</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Results showed that believing one had taken the substance resulted in [performance] times almost as fast as those associated with consuming the substance itself. In contrast, taking the substance without knowledge yielded no significant performance increment. </span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">When participation in a study prompts a physical response from a participant, it is difficult to isolate the effects of the explanatory variable. To counter the power of suggestion, researchers set aside one treatment group as a <strong>control group</strong>.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">This group is given a <strong>placebo </strong>treatment, a treatment that cannot influence the response variable. The control group helps researchers balance the effects of being in an experiment with the effects of the active treatments. Of course, if you are participating in a study and you know that you are receiving a pill that contains no actual medication, then the power of suggestion is no longer a factor. <strong>Blinding </strong>in a randomized experiment designed to reduce bias by hiding information. When a person involved in a research study is blinded, he does not know who is receiving the active treatment(s) and who is receiving the placebo treatment. A <strong>double-blind experiment </strong>is one in which both the subjects and the researchers involved with the subjects are blinded.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Sometimes, it is neither possible nor ethical for researchers to conduct experimental studies. For example, if you want to investigate whether malnutrition affects elementary school performance in children, it would not be appropriate to assign an experimental group to be malnourished. In these cases, <strong>observational studies </strong>or <strong>surveys </strong>may be used. In an observational study, the researcher does not directly manipulate the independent variable. Instead, he or she takes recordings and measurements of naturally occurring phenomena. By sorting these data into control and experimental conditions, the &nbsp;reacher&rsquo;s measurements consist of questionnaires that are answered by the research participants.</span></p>','','1','1.4',NULL,'1','2','1','0','1','2021-06-12 11:43:33','2021-06-12 11:43:33'),(2177,97,'1.4.1 EXAMPLES','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;1.21</span></strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:white\">Example 1.20</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Researchers want to investigate whether taking aspirin regularly reduces the risk of a heart attack. 400 men between the ages of 50 and 84 are recruited as participants. The men are divided randomly into two groups: one group will take aspirin, and the other group will take a placebo. Each man takes one pill each day for three years, but he does not know whether he is taking aspirin or the placebo. At the end of the study, researchers count the number of men in each group who have had heart attacks.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Identify the following values for this study: population, sample, experimental units, explanatory variable, response variable, treatments.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#26397f\">Solution 1.21</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><em><span style=\"color:black\">population </span></em></strong><span style=\"color:black\">is men aged 50 to 84.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><em><span style=\"color:black\">sample </span></em></strong><span style=\"color:black\">is the 400 men who participated.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><em><span style=\"color:black\">experimental units </span></em></strong><span style=\"color:black\">are the individual men in the study.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><em><span style=\"color:black\">explanatory variable </span></em></strong><span style=\"color:black\">is oral medication.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><em><span style=\"color:black\">treatments </span></em></strong><span style=\"color:black\">are aspirin and a placebo.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The </span><strong><em><span style=\"color:black\">response variable </span></em></strong><span style=\"color:black\">is whether a subject had a heart attack.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;1.22</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The Smell &amp; Taste Treatment and Research Foundation conducted a study to investigate whether smell can affect learning. Subjects completed mazes multiple times while wearing masks. They completed the pencil and paper mazes three times wearing floral-scented masks, and three times with unscented masks. Participants were assigned at random to wear the floral mask during the first three trials or during the last three trials. For each trial, researchers recorded the time it took to complete the maze and the subject&rsquo;s impression of the mask&rsquo;s scent: positive, negative, or neutral.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">Describe the explanatory and response variables in this study.</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">What are the treatments?</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">Identify any lurking variables that could interfere with this study.</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\">Is it possible to use blinding in this study?</span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;1.22</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ol style=\"list-style-type:lower-alpha\">\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">The explanatory variable is scent, and the response variable is the time it takes to complete the maze.</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">There are two treatments: a floral-scented mask and an unscented mask.</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">All subjects experienced both treatments. The order of treatments was randomly assigned so there were no differences between the treatment groups. Random assignment eliminates the problem of lurking variables.</span></p>\n	</li>\n	<li style=\"text-align:justify\">\n	<p><span style=\"font-size:14px\">Subjects will clearly know whether they can smell flowers or not, so subjects cannot be blinded in this study. Researchers timing the mazes can be blinded, though. The researcher who is observing a subject will not know which mask is being worn.</span></p>\n	</li>\n</ol>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Example 1.23</strong><span style=\"color:white\"><strong>&nbsp;1.</strong>22</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">A researcher wants to study the effects of birth order on personality. Explain why this study could not be conducted as a randomized experiment. What is the main problem in a study that cannot be designed as a randomized experiment?</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>Solution 1.23</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The explanatory variable is birth order. You cannot randomly assign a person&rsquo;s birth order. Random assignment eliminates the impact of lurking variables. When you cannot assign subjects to treatment groups at random, there will be differences between the groups other than the explanatory variable.</span></span></p>','','1','1.4.1',NULL,'1','2','1','0','1','2021-06-21 10:31:16','2021-06-21 16:01:16'),(2178,97,'1.4.2 ETHICS','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The widespread misuse and misrepresentation of statistical information often gives the field a bad name. Some say that &ldquo;numbers don&rsquo;t lie,&rdquo; but the people who use numbers to support their claims often do.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">A recent investigation of famous social psychologist, Diederik Stapel, has led to the retraction of his articles from some of the world&rsquo;s top journals including, </span><em><span style=\"color:black\">Journal of Experimental Social Psychology, Social Psychology, Basic and Applied Social Psychology, British Journal of Social Psychology, </span></em><span style=\"color:black\">and the magazine </span><em><span style=\"color:black\">Science</span></em><span style=\"color:black\">. Diederik Stapel is a former professor at Tilburg University in the Netherlands. Over the past two years, an extensive investigation involving three universities where Stapel has worked concluded that the psychologist is guilty of fraud on a colossal scale. Falsified data taints over 55 papers he authored and 10 Ph.D. dissertations that he supervised.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><em><span style=\"color:black\">Stapel did not deny that his deceit was driven by ambition. But it was more complicated than that, he told me. He insisted that he loved social psychology but had been frustrated by the messiness of experimental data, which rarely led to clear conclusions. His lifelong obsession with elegance and order, he said, led him to concoct results that journals found attractive. &ldquo;It was a quest for aesthetics, for beauty&mdash;instead of the truth,&rdquo; he said. He described his behavior as an addiction that drove him to carry out acts of increasingly daring fraud</span></em><span style=\"color:black\">.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">The committee investigating Stapel concluded that he is guilty of several practices including</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; creating datasets, which largely confirmed the prior expectations,</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; altering data in existing datasets,</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; changing measuring instruments without reporting the change, and</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; misrepresenting the number of experimental subjects.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Clearly, it is never acceptable to falsify data the way this researcher did. Sometimes, however, violations of ethics are not as easy to spot.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Researchers have a responsibility to verify that proper methods are being followed. The report describing the investigation of Stapel&rsquo;s fraud states that, &ldquo;statistical flaws frequently revealed a lack of familiarity with elementary statistics.&rdquo; Many of Stapel&rsquo;s co-authors should have spotted irregularities in his data. Unfortunately, they did not know very much about statistical analysis, and they simply trusted that he was collecting and reporting data properly.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Many types of statistical fraud are difficult to spot. Some researchers simply stop collecting data once they have just enough to prove what they had hoped to prove. They don&rsquo;t want to take the chance that a more extensive study would complicate their lives by producing data contradicting their hypothesis.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Professional organizations, like the American Statistical Association, clearly define expectations for researchers. There are even laws in the federal code about the use of research data.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">When a statistical study uses human participants, as in medical studies, both ethics and the law dictate that researchers should be mindful of the safety of their research subjects. The U.S. Department of Health and Human Services oversees federal regulations of research studies with the aim of protecting participants. When a university or other research institution engages in research, it must ensure the safety of all human subjects. For this reason, research institutions establish oversight committees known as </span><strong><span style=\"color:black\">Institutional Review Boards (IRB)</span></strong><span style=\"color:black\">. All planned studies must be approved in advance by the IRB.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Key protections that are mandated by law include the following:</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">&bull; Risks to participants must be minimized and reasonable with respect to projected benefits.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">&bull; Participants must give </span><strong><span style=\"color:black\">informed consent</span></strong><span style=\"color:black\">. This means that the risks of participation must be clearly explained to the subjects of the study. Subjects must consent in writing, and researchers are required to keep documentation of their consent.</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; Data collected from individuals must be guarded carefully to protect their privacy.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">These ideas may seem fundamental, but they can be very difficult to verify in practice. Is removing a participant&rsquo;s name from the data record sufficient to protect privacy? Perhaps the person&rsquo;s identity could be discovered from the data that remains. What happens if the study does not proceed as planned and risks arise that were not anticipated? When is informed consent really necessary? Suppose your doctor wants a blood sample to check your cholesterol level. Once the sample has been tested, you expect the lab to dispose of the remaining blood. At that point the blood becomes biological waste. Does a researcher have the right to take it for use in a study?</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">It is important that students of statistics take time to consider the ethical questions that arise in statistical studies. How prevalent is fraud in statistical studies? You might be surprised&mdash;and disappointed. Vigilance against fraud requires knowledge. Learning the basic theory of statistics will empower you to analyze statistical studies critically.</span></span><span style=\"font-size:14px\"><span style=\"color:white\">Exam</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:white\">Example 1.23</span></span></p>\n\n<p><span style=\"font-size:14px\"><strong>Example 1.24</strong></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Describe the unethical behavior in each example and describe how it could impact the reliability of the resulting data. Explain how the problem should be corrected.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">A researcher is collecting data in a community.</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">a. She selects a block where she is comfortable walking because she knows many of the people living on the street.</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">b. No one seems to be home at four houses on her route. She does not record the addresses and does not return at a later time to try to find residents at home.</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">c. She skips four houses on her route because she is running late for an appointment. When she gets home, she fills in the forms by selecting random answers from other residents in the neighborhood.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong>Solution 1.24</strong></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">a. By selecting a convenient sample, the researcher is intentionally selecting a sample that could be biased. Claiming that this sample represents the community is misleading. The researcher needs to select areas in the community at random.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">b. Intentionally omitting relevant data will create bias in the sample. Suppose the researcher is gathering information about jobs and child care. By ignoring people who are not home, she may be missing data from working families that are relevant to her study. She needs to make every effort to interview all members of the target sample.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">c. It is never acceptable to fake data. Even though the responses she uses are </span><em><span style=\"color:black\">real </span></em><span style=\"color:black\">responses provided by other participants, the duplication is fraudulent and can create bias in the data. She needs to work diligently to interview everyone on her route.</span><span style=\"color:white\">pl</span></span></p>','','1','1.4.2',NULL,'1','2','1','0','1','2021-06-21 10:32:59','2021-06-21 16:02:59'),(2179,97,'1.5 Data Collection Experiment','','single','html','<p><span style=\"font-size:14px\">Student Learning Outcomes</span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; The student will demonstrate the systematic sampling technique.</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; The student will construct relative frequency tables.</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">&bull; The student will interpret results and their differences from different data groupings.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong>Movie Survey</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Get a class roster/list. Randomly mark a person&rsquo;s name, and then mark every fourth name on the list until you get 12 names. You may have to go back to the start of the list. For each name marked, record the number of movies they saw at the theater last month.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong>Order the Data</strong></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Complete the two relative frequency tables below using your class data</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234787931623478793.png\" style=\"height:345px; width:900px\" /></span></span></p>\n\n<p><span style=\"font-size:14px\"><strong><span style=\"color:#26397f\">Table 1.20 Frequency of Number of Movies Viewed</span></strong></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong><span style=\"color:#26397f\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234788301623478830.png\" style=\"height:211px; width:900px\" /></span></strong></span></p>\n\n<p><span style=\"font-size:14px\"><strong>Table 1.21 Frequency of Number of Movies Viewed</strong></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">1. Using the tables, find the percent of data that is at most two. Which table did you use and why?</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">2. Using the tables, find the percent of data that is at most three. Which table did you use and why?</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">3. Using the tables, find the percent of data that is more than two. Which table did you use and why?</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">4. Using the tables, find the percent of data that is more than three. Which table did you use and why?</span><span style=\"color:white\">e 1</span></span></p>','','1','1.5',NULL,'1','2','1','0','1','2021-06-21 10:34:30','2021-06-21 16:04:30'),(2180,97,'1.6 Sampling Experiment','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>&nbsp;&nbsp; Student Learning Outcomes</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:18px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">&bull; The student will demonstrate the simple random, systematic, stratified, and cluster sampling techniques.</span></span></p>\n\n<p style=\"margin-left:54px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">&bull; The student will explain the details of each procedure used.</span></span></p>\n\n<p style=\"margin-left:18px; text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:18px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">In this lab, you will be asked to pick several random samples of restaurants. In each case, describe your procedure briefly, including how you might have used the random number generator, and then list the restaurants in the sample you obtained.</span></span></p>\n\n<p style=\"margin-left:18px; text-align:justify\">&nbsp;</p>\n\n<p style=\"margin-left:18px; text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Restaurants Stratified by City and Entree Cost</strong></span></span></p>\n\n<p style=\"margin-left:18px; text-align:justify\">&nbsp;</p>\n\n<table align=\"center\" cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:31px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:7px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Entree Cost</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:31px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:5px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Under Rs 1000</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:31px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Rs.1000 To Under Rs.1500</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:31px; vertical-align:top; width:127px\">\n			<div style=\"margin-left:22px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Rs.1500 To Underrs.2000</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:31px; vertical-align:top; width:144px\">\n			<div style=\"margin-left:37px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Over&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Rs.2000</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:41px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:7px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Mumbai</span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:41px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Lemon Leaf, Andheri West</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:41px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Global Buffet Mumbai</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:41px; vertical-align:top; width:127px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:#f0f0f0\"><span style=\"color:black\">Wasabi By Morimoto</span></span></span></div>\n\n			<div style=\"margin-left:22px; text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:41px; vertical-align:top; width:144px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:#2e74b5\"><em><span style=\"color:black\">&nbsp;Estella, Juhu</span></em></span></span></span></div>\n\n			<div style=\"margin-left:37px; text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:47px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Pune</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:47px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"background-color:white\"><span style=\"color:black\">Malaka Spice:&nbsp;Meera Nagar Pune</span></span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:47px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\"><a href=\"https://magicpin.in/Pune/Kalyani-Nagar/Restaurant/Mineority-By-Saby/store/85466/\" target=\"_blank\"><span style=\"color:black\">Mineority By Saby</span></a></span></span></span></div>\n\n			<div style=\"margin-left:20px; text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:47px; vertical-align:top; width:127px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Village-The Soul Of India</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:47px; vertical-align:top; width:144px\">\n			<div style=\"margin-left:37px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Pasha &ndash; JW Marriott Pune</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:53px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Nagpur</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:53px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Haldiram&rsquo;s, Nagpur</span></span></span></div>\n\n			<div style=\"margin-left:20px; text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:53px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Naivedhyam, Nagpur</span></span></span></div>\n\n			<div style=\"margin-left:20px; text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:53px; vertical-align:top; width:127px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Veeraswami, Nagpur</span></span></span></div>\n\n			<div style=\"margin-left:20px; text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:53px; vertical-align:top; width:144px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Reddy&rsquo;s Gokul Brindavan Restaurant, Nagpur</span></span></span></div>\n\n			<div style=\"margin-left:37px; text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Nashik</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Chai Tapri</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">The Cobble Street</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; vertical-align:top; width:127px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Shri Krishna Vijay Restaurant</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; vertical-align:top; width:144px\">\n			<div style=\"margin-left:37px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Barbeque Ille</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:25px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Thane</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:25px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">180 Degrees</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:25px; vertical-align:top; width:136px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Kangan</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:25px; vertical-align:top; width:127px\">\n			<div style=\"margin-left:20px; text-align:center\"><span style=\"font-size:28px\"><span style=\"background-color:white\"><span style=\"color:black\">Fleur Restaurant</span></span></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:25px; vertical-align:top; width:144px\">\n			<div style=\"margin-left:37px; text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Prego</span></span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Table 1.22 Restaurants Used in Sample</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>A Simple Random Sample</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Pick a </span><strong><span style=\"color:black\">simple random sample </span></strong><span style=\"color:black\">of 15 restaurants.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">1. Describe your procedure.</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">2. Complete the table with your sample.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234790801623479080.png\" style=\"height:429px; width:900px\" /></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>A Systematic Sample</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Pick a </span><strong><span style=\"color:black\">systematic sample </span></strong><span style=\"color:black\">of 15 restaurants.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">1. Describe your procedure.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">2. Complete the table with your sample.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234791091623479109.png\" style=\"height:407px; width:900px\" /></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>A Stratified Sample</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Pick a </span><strong><span style=\"color:black\">stratified sample</span></strong><span style=\"color:black\">, by city, of 20 restaurants. Use 25 percent of the restaurants from each stratum. Round to the nearest whole number.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">1. Describe your procedure.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">2. Complete the table with your sample.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234791461623479146.png\" style=\"height:344px; width:900px\" /></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>A Stratified Sample</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Pick a </span><strong><span style=\"color:black\">stratified sample</span></strong><span style=\"color:black\">, by entree cost, of 21 restaurants. Use 25 percent of the restaurants from each stratum. Round</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Chapter 1 | </span></span><span style=\"font-size:14px\"><span style=\"color:black\">to the nearest whole number.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">1. Describe your procedure.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">2. Complete the table with your sample.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234791851623479185.png\" style=\"height:388px; width:900px\" /></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>A Cluster Sample</strong></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Pick a </span><strong><span style=\"color:black\">cluster sample </span></strong><span style=\"color:black\">of restaurants from two cities. The number of restaurants will vary.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">1. Describe your procedure.</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">2. Complete the table with your sample.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16234792301623479230.png\" style=\"height:322px; width:900px\" /></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>','','1','1.6',NULL,'1','2','1','0','1','2021-06-21 10:38:56','2021-06-21 16:08:56'),(2181,97,'The science of statistics deals with the collection, analysis, interpretation, and presentation of data.','','multi','single','','','1','1.1',NULL,'1','1','1','0','1','2021-06-12 13:44:33','2021-06-12 13:44:33'),(2182,97,'Finding an average is a way to summarize data.','','multi','single','','','1','1.1',NULL,'1','1','1','0','1','2021-06-12 13:45:12','2021-06-12 13:45:12'),(2183,97,'Statistical models cannot be used to predict life’s more uncertain situations.','','multi','single','','','1','1.1',NULL,'2','1','1','0','1','2021-06-12 13:45:54','2021-06-12 13:45:54'),(2184,97,'When we throw a coin then what is the probability of getting head?','','multi','single','','','1','1.1.1',NULL,'1','1','1','0','1','2021-06-19 11:39:37','2021-06-19 17:09:37'),(2185,97,'We can use probability is buying a lottery ticket.','','multi','single','','','1','1.1.1',NULL,'1','1','1','0','1','2021-06-12 13:47:57','2021-06-12 13:47:57'),(2186,97,'Which of the following statements best describes the relationship between a parameter and a statistic?','','multi','single','','','1','1.1.2',NULL,'2','1','1','0','1','2021-06-12 13:49:37','2021-06-12 13:49:37'),(2187,97,'The idea of sampling is to __________ of the larger population and study that portion to gain information about the population.','','multi','single','','','1','1.1.2',NULL,'1','1','1','0','1','2021-06-12 13:50:56','2021-06-12 13:50:56'),(2188,97,'To be a representative sample it means','','multi','single','','','1','1.1.2',NULL,'4','1','1','0','1','2021-06-12 13:52:47','2021-06-12 13:52:47'),(2189,97,'What variable due we take in Numerical variables?','','multi','single','','','1','1.1.2',NULL,'1','1','1','0','1','2021-06-19 11:43:06','2021-06-19 17:13:06'),(2190,97,'Quantitative data may be either','','multi','single','','','1','1.2',NULL,'1','1','1','0','1','2021-06-12 13:56:20','2021-06-12 13:56:20'),(2191,97,'Qualitative data are also often called','','multi','single','','','1','1.2',NULL,'1','1','1','0','1','2021-06-12 13:58:06','2021-06-12 13:58:06'),(2192,97,'In each form of random sampling each member of a population has an equal chance of being selected for the sample.','','multi','single','','','1','1.2.5',NULL,'1','1','1','0','1','2021-06-12 13:59:29','2021-06-12 13:59:29'),(2193,97,'The difficult method of sampling is Simple Random Sample:','','multi','single','','','1','1.2.5',NULL,'2','1','1','0','1','2021-06-12 14:00:37','2021-06-12 14:00:37'),(2194,97,'In stratified random sample the whole population is divided into smaller groups called strata.','','multi','single','','','1','1.2.5',NULL,'1','1','1','0','1','2021-06-16 05:41:18','2021-06-16 11:11:18'),(2195,97,'Sampling with Replacement is once a member of the population is selected for inclusion in a sample, a new member is returned to the population for the selection of the next individual.','','multi','single','','','1','1.2.5',NULL,'2','1','1','0','1','2021-06-12 14:02:07','2021-06-12 14:02:07'),(2196,97,'The size of the sample can be one of the reason for sampling errors.','','multi','single','','','1','1.2.5',NULL,'1','1','1','0','1','2021-06-12 14:03:16','2021-06-12 14:03:16'),(2197,97,'A defective counting device can cause a sampling error.','','multi','single','','','1','1.2.5',NULL,'2','1','1','0','1','2021-06-12 14:04:25','2021-06-12 14:04:25'),(2198,97,'An instructor takes her sample by gathering data on five randomly selected students from each math class of CCIS college. The type of sampling she used is','','multi','single','','','1','1.2.5',NULL,'2','1','1','0','1','2021-06-12 14:05:44','2021-06-12 14:05:44'),(2199,97,'A sample that is not representative of the population is _________.','','multi','single','','','1','1.2.5',NULL,'1','1','1','0','1','2021-06-12 14:06:57','2021-06-12 14:06:57'),(2200,97,'Misleading use of data may be due to','','multi','single','','','1','1.2.5',NULL,'4','1','1','0','1','2021-06-12 14:08:14','2021-06-12 14:08:14'),(2201,97,'The lowest level of measurement is','','multi','single','','','1','1.3.1',NULL,'2','1','1','0','1','2021-06-12 14:09:33','2021-06-12 14:09:33'),(2202,97,'Which scale level can be ordered?','','multi','single','','','1','1.3.1',NULL,'1','1','1','0','1','2021-06-12 14:10:40','2021-06-12 14:10:40'),(2203,97,'Data that is measured using a nominal scale is qualitative (categorical).','','multi','single','','','1','1.3.1',NULL,'2','1','1','0','1','2021-06-12 14:11:44','2021-06-12 14:11:44'),(2204,97,'Each value of the explanatory variable used in an experiment is called a treatment','','multi','single','','','1','1.4',NULL,'1','1','1','0','1','2021-06-12 14:12:43','2021-06-12 14:12:43'),(2205,97,'Lurking variables are __________ that can cloud a study.','','multi','single','','','1','1.4',NULL,'2','1','1','0','1','2021-06-12 14:13:54','2021-06-12 14:13:54'),(2206,97,'Blinding in a randomized experiment designed to reduce bias by revealing all the information.','','multi','single','','','1','1.4',NULL,'2','1','1','0','1','2021-06-12 14:14:39','2021-06-12 14:14:39'),(2207,97,'A placebo treatment is a treatment that can influence the response variable.','','multi','single','','','1','1.4',NULL,'2','1','1','0','1','2021-06-12 14:15:19','2021-06-12 14:15:19'),(2208,97,'A double-blind experiment is one in which both the subjects and the researchers involved with the subjects are blinded.','','multi','single','','','1','1.4',NULL,'1','1','1','0','1','2021-06-12 14:16:03','2021-06-12 14:16:03'),(2209,97,'2 DESCRIPTIVE STATISTICS	INTRODUCTION','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Once you have collected data, what will you do with it? Data can be described and presented in many different formats. For example, suppose you are interested in buying a house in a particular area. You may have no clue about the house prices, so you might ask your real estate agent to give you a sample data set of prices. Looking at all the prices in the sample often is overwhelming. A better way might be to look at the median price and the variation of prices. The median and variation are just two ways that you will learn to describe data. Your agent might also provide you with a graph of the data.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called&nbsp;<strong>&quot;Descriptive Statistics.&quot;</strong>&nbsp;You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">A statistical graph is a tool that helps you learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a mass of numbers because we can see where data clusters and where there are only a few data values. Newspapers and the Internet use graphs to show trends and to enable readers to compare facts and figures quickly. Statisticians often graph data first to get a picture of the data. Then, more formal tools may be applied.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Some of the types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon (a type of broken line graph), the pie chart, and the box plot. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots</span><span style=\"color:#424242\">.</span></span></p>','','1','2',NULL,'1','2','1','0','1','2021-06-15 15:37:37','2021-06-15 15:37:37'),(2210,97,'2.1 Stem-and-Leaf Graphs (Stemplots)','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">One simple graph, the&nbsp;<strong>stem-and-leaf graph</strong>&nbsp;or&nbsp;<strong>stemplot</strong>, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a&nbsp;<strong>final significant digit</strong>. For example, 23 has stem two and leaf three. The number 432 has stem 43 and leaf two. Likewise, the number 5,432 has stem 543 and leaf two. The decimal 9.3 has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;2.1</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">For Susan Dean&#39;s spring pre-calculus class, scores for the first exam were as follows (smallest to largest): 33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table border=\"1\" cellspacing=\"0\" style=\"width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><strong>Table2.1 Stem-and-Leaf Graph</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Stem</strong></span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Leaf</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2 9 9</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3 5 5</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1 3 7 8 8 9 9</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">7</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2 3 4 8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0 3 8 8 8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">9</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0 2 4 4 4 4 6</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">10</span></div>\n			</td>\n			<td>\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The stemplot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26%&nbsp;(831)(831)&nbsp;were in the 90s or 100, a fairly high number of As.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The stemplot is a quick way to graph data and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An&nbsp;outlier&nbsp;is an observation of data that does not fit the rest of the data. It is sometimes called an&nbsp;extreme<strong> value.</strong>&nbsp;When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later</span><span style=\"color:#424242\">.</span></span></p>','','1','2.1',NULL,'1','2','1','0','1','2021-06-21 10:43:15','2021-06-21 16:13:15'),(2211,97,'2.1.1 Examples','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>EXAMPLE&nbsp;2.2</strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The data are the distances (in kilometers) from a home to local supermarkets. Create a stemplot using the data:</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">1.1; 1.5; 2.3; 2.5; 2.7; 3.2; 3.3; 3.3; 3.5; 3.8; 4.0; 4.2; 4.5; 4.5; 4.7; 4.8; 5.5; 5.6; 6.5; 6.7; 12.3</span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">Do the data seem to have any concentration of values? </span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#000000\">Solution&nbsp;2.2</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The value 12.3 may be an outlier. Values appear to concentrate at three and four kilometers.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table align=\"left\" cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; margin-left:9px; margin-right:9px; width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><strong>TABLE 2.2</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:24px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Stem</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:24px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Leaf</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1&nbsp;5</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3&nbsp;5&nbsp;7</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2&nbsp;3&nbsp;3&nbsp;5&nbsp;8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:23px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:23px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0&nbsp;2&nbsp;5&nbsp;5&nbsp;7&nbsp;8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5&nbsp;6</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5&nbsp;7</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">7</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">9</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:23px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">10</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:23px; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">11</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">12</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:24px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong><span style=\"color:#000000\">EXAMPLE&nbsp;2.3</span></strong></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">A&nbsp;<strong>side-by-side stem-and-leaf plot</strong>&nbsp;allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the stems.&nbsp;</span><a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#M01_Ch02_tbl005\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Table 2.4</span></a><span style=\"color:black\">&nbsp;and&nbsp;</span><a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#M01_Ch02_tbl006\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Table 2.5</span></a><span style=\"color:black\">&nbsp;show the ages of presidents at their inauguration and at their death. Construct a side-by-side stem-and-leaf plot using this data</span><span style=\"color:#424242\">.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong><span style=\"color:#000000\">Solution&nbsp;1</span></strong></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\">The value 12.3 may be an outlier. Values appear to concentrate at 3 and 4 kilometers</span></p>\n\n<p>&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><strong>Table2.3</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:18px; vertical-align:bottom; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>President</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:18px; vertical-align:bottom; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Age</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:18px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>President</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:18px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Age</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:18px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>President</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:18px; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Age</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Washington</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">57</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Lincoln</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">52</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Hoover</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">54</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:35px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">J. Adams</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">61</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">A. Johnson</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">56</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">F. Roosevelt</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">51</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:17px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Jefferson</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">57</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Grant</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">46</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Truman</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:17px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">60</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Madison</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">57</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Hayes</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">54</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Eisenhower</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">62</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Monroe</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">58</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Garfield</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">49</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Kennedy</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">43</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">J. Q. Adams</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">57</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Arthur</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">51</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">L. Johnson</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">55</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Jackson</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">61</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Cleveland</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">47</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Nixon</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">56</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:35px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Van Buren</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">54</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">B. Harrison</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">55</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Ford</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">61</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">W. H. Harrison</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">68</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Cleveland</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">55</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Carter</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">52</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Tyler</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">51</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">McKinley</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">54</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Reagan</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">69</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:35px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Polk</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">49</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">T. Roosevelt</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">42</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">G.H.W. Bush</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:35px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">64</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Taylor</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">64</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Taft</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">51</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Clinton</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">47</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Fillmore</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">50</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Wilson</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">56</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">G. W. Bush</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">54</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Pierce</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">48</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Harding</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">55</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Obama</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">47</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:18px; width:132px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Buchanan</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px; width:71px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">65</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">Coolidge</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">51</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:18px\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"background:#ededed; border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><span style=\"color:#000000\"><strong>Table2.4 Presidential Age at Death</strong></span></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">President</span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong><span style=\"color:black\">Age</span></strong></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong><span style=\"color:black\">President</span></strong></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong><span style=\"color:black\">Age</span></strong></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong><span style=\"color:black\">President</span></strong></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong><span style=\"color:black\">Age</span></strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Washington</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">67</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Lincoln</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">56</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Hoover</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">90</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">J. Adams</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">90</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">A. Johnson</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">66</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">F. Roosevelt</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">63</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Jefferson</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">83</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Grant</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">63</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Truman</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">88</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Madison</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">85</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Hayes</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">70</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Eisenhower</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">78</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Monroe</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">73</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Garfield</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">49</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Kennedy</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">46</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">J. Q. Adams</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">80</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Arthur</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">56</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">L. Johnson</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">64</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Jackson</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">78</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Cleveland</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">71</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Nixon</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">81</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Van Buren</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">79</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">B. Harrison</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">67</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Ford</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">93</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">W. H. Harrison</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">68</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Cleveland</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">71</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Reagan</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">93</span></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Tyler</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">71</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">McKinley</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">58</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Polk</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">53</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">T. Roosevelt</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">60</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Taylor</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">65</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Taft</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">72</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Fillmore</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">74</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Wilson</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">67</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Pierce</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">64</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Harding</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">57</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Buchanan</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">77</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">Coolidge</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><span style=\"color:black\">60</span></span></div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"background-color:#ededed; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;1</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Ages at Inauguration</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; text-align:center; vertical-align:bottom\">\n			<div>&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Ages at Death</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">9 9 8 7 7 7 6 3 2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6 9</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8 7 7 7 7 6 6 6 5 5 5 5 4 4 4 4 4 2 1 1 1 1 1 0</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3 6 6 7 7 8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">9 5 4 4 2 1 1 1 0</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0 0 3 3 4 4 5 6 7 7 7 8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">7</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0 0 1 1 1 4 7 8 8 9</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0 1 3 5 8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; text-align:center\">\n			<div>&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">9</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0 0 3 3</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Notice that the leaf values increase in order, from right to left, for leaves shown to the left of the stem, while the leaf values increase in order from left to right, for leaves shown to the right of the stem.</span></span></p>','','1','2.1.1',NULL,'1','2','1','0','1','2021-06-21 10:52:31','2021-06-21 16:22:31'),(2212,97,'2.1.2 Line graph','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">Another type of graph that is useful for specific data values is a&nbsp;<strong>line graph</strong>. In the particular line graph shown in&nbsp;<a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#example4\"><span style=\"color:black\">Example 2.4</span></a>, the&nbsp;<strong><em>x</em>-axis</strong>&nbsp;(horizontal axis) consists of&nbsp;<strong>data values</strong>&nbsp;and the&nbsp;<strong><em>y</em>-axis</strong>&nbsp;(vertical axis) consists of&nbsp;<strong>frequency points</strong>. The frequency points are connected using line segments.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>EXAMPLE&nbsp;</strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">In a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his or her chores. The results are shown in&nbsp;</span><a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#M01_Ch02_tbl008\"><span style=\"color:black\">Table 2.6</span></a><span style=\"color:black\">&nbsp;and in&nbsp;</span><a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#M01_Ch02_fig001\"><span style=\"color:black\">Figure 2.2</span></a><span style=\"color:black\">.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><strong>Table2.6</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Number of times teenager is reminded</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Frequency</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">14</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">7</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16237539291623753929.jpg\" style=\"height:504px; width:800px\" /></p>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Figure&nbsp;2.2</strong></span></p>','','1','2.1.2',NULL,'1','2','1','0','1','2021-06-21 10:54:09','2021-06-21 16:24:09'),(2213,97,'2.1.3 Bar graphs','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:black\">Bar graphs</span></strong><span style=\"color:black\">&nbsp;consist of bars that are separated from each other. The bars can be rectangles or they can be rectangular boxes (used in three-dimensional plots), and they can be vertical or horizontal. The&nbsp;<strong>bar graph</strong>&nbsp;shown in&nbsp;<a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#example5\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Example 2.5</span></a>&nbsp;has age groups represented on the&nbsp;<em><strong>x</strong></em><strong>-axis</strong>&nbsp;and proportions on the&nbsp;<em><strong>y</strong></em><strong>-axis</strong>.</span></span></span></p>','','1','2.1.3',NULL,'1','2','1','0','1','2021-06-15 16:19:35','2021-06-15 16:19:35'),(2214,97,'2.1.4 EXAMPLES','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;2.5</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">By the end of 2011, Facebook had over 146 million users in the United States.&nbsp;<a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#M01_Ch02_tbl010\" style=\"color:blue; text-decoration:underline\"><span style=\"color:#027eb5\">Table 2.8</span></a>&nbsp;shows three age groups, the number of users in each age group, and the proportion (%) of users in each age group. Construct a bar graph using this data.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><span style=\"font-size:14px\"><strong>Table2.8</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Age groups</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Number of Facebook users</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Proportion (%) of Facebook users</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">13&ndash;25</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">65,082,280</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">45%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">26&ndash;44</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">53,300,200</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">36%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">45&ndash;64</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">27,885,100</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">19%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#333333\">Solution&nbsp;1</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#333333\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16237545431623754543.jpg\" style=\"height:597px; width:800px\" /></span></span></p>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><strong><span style=\"color:#424242\">Figure&nbsp;2.3</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;2.6</span></strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The columns in&nbsp;</span><a href=\"https://openstax.org/books/statistics/pages/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs#M01_Ch02_tbl012\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Table 2.11</span></a><span style=\"color:black\">&nbsp;contain the race or ethnicity of students in U.S. public schools for the class of 2011, percentages for the Advanced Placement (AP) examinee population for that class, and percentages for the overall student population. Create a bar graph with the student race or ethnicity (qualitative data) on the&nbsp;<em>x</em>-axis and the AP examinee population percentages on the&nbsp;<em>y</em>-axis.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<div><span style=\"font-size:14px\"><strong>Table2.11</strong></span></div>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Race/Ethnicity</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>AP Examinee Population</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Overall Student Population</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">1 = AP</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">10.3%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">5.7%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">2 = Maharashtra</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">9.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">14.7%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">3 = MP</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">17.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">17.6%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">4 = Orissa</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">0.6%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">1.1%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">5 = TN</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">57.1%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">59.2%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">6 = Rajasthan</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">6.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">1.7%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16237547091623754709.jpg\" style=\"height:559px; width:800px\" /></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>EXAMPLE&nbsp;<span style=\"color:#2f5496\">2.7</span></strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Below is a two-way table showing the types of pets owned by men and women:</span></span></p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<div><span style=\"font-size:14px\"><strong>Table2.12</strong></span></div>\n	</caption>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Dogs</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Cats</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Fish</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Total</strong></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Men</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Women</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">6</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">12</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Total</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">20</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Given these data, calculate the conditional distributions for the subpopulation of men who own each pet type</span><span style=\"color:#424242\">.</span></span></p>\n\n<p><span style=\"font-size:14px\"><strong><span style=\"color:#4472c4\">Solution&nbsp;1</span></strong></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Men who own dogs = 4/8 = 0.5</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Men who own cats = 2/8 = 0.25</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Men who own fish = 2/8 = 0.25</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Note: The sum of all of the conditional distributions must equal one. In this case, 0.5 + 0.25 + 0.25 = 1; therefore, the solution &quot;checks&quot;.</span></span></p>','','1','2.1.4',NULL,'1','2','1','1','1','2021-06-21 10:58:38','2021-06-21 16:28:38'),(2215,97,'2.1.4 EXAMPLES','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;2.5</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">By the end of 2011, Facebook had over 146 million users in the United States.&nbsp;<a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#M01_Ch02_tbl010\" style=\"color:blue; text-decoration:underline\"><span style=\"color:#027eb5\">Table 2.8</span></a>&nbsp;shows three age groups, the number of users in each age group, and the proportion (%) of users in each age group. Construct a bar graph using this data.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><strong>Table2.8</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Age groups</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Number of Facebook users</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Proportion (%) of Facebook users</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">13&ndash;25</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">65,082,280</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">45%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">26&ndash;44</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">53,300,200</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">36%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">45&ndash;64</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">27,885,100</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">19%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><strong><span style=\"color:#333333\">Solution&nbsp;1</span></strong></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#333333\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16237545431623754543.jpg\" style=\"height:597px; width:800px\" /></span></span></p>\n\n<p style=\"text-align:center\"><span style=\"font-size:14px\"><strong><span style=\"color:#424242\">Figure&nbsp;2.3</span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;2.6</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The columns in&nbsp;</span><a href=\"https://openstax.org/books/statistics/pages/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs#M01_Ch02_tbl012\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Table 2.11</span></a><span style=\"color:black\">&nbsp;contain the race or ethnicity of students in U.S. public schools for the class of 2011, percentages for the Advanced Placement (AP) examinee population for that class, and percentages for the overall student population. Create a bar graph with the student race or ethnicity (qualitative data) on the&nbsp;<em>x</em>-axis and the AP examinee population percentages on the&nbsp;<em>y</em>-axis.</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><strong>Table2.11</strong></span></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Race/Ethnicity</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>AP Examinee Population</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Overall Student Population</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1 = AP</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">10.3%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5.7%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2 = Maharashtra</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">9.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">14.7%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">3 = MP</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">17.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">17.6%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4 = Orissa</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">0.6%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1.1%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">5 = TN</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">57.1%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">59.2%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6 = Rajasthan</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">1.7%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16237547091623754709.jpg\" style=\"height:559px; width:800px\" /></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong>EXAMPLE&nbsp;<span style=\"color:#000000\">2.7</span></strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Below is a two-way table showing the types of pets owned by men and women:</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><span style=\"font-size:20px\"><strong>Table2.12</strong></span></p>\n	</caption>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Dogs</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Cats</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Fish</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Total</strong></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Men</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Women</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">6</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">12</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\"><strong>Total</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:28px\">20</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Given these data, calculate the conditional distributions for the subpopulation of men who own each pet type</span><span style=\"color:#424242\">.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>Solution&nbsp;1</strong></span></span></p>\n\n<p>&nbsp;</p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Men who own dogs = 4/8 = 0.5</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Men who own cats = 2/8 = 0.25</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Men who own fish = 2/8 = 0.25</span></span></p>\n\n<p><span style=\"font-size:14px\"><span style=\"color:black\">Note: The sum of all of the conditional distributions must equal one. In this case, 0.5 + 0.25 + 0.25 = 1; therefore, the solution &quot;checks&quot;.</span></span></p>','','1','2.1.4',NULL,'1','2','1','0','1','2021-06-21 10:59:48','2021-06-21 16:29:48'),(2216,97,'2.1.5 EXAMPLES','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:#000000\"><strong>EXAMPLE&nbsp;2.5</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">By the end of 2011, Facebook had over 146 million users in the United States.&nbsp;<a href=\"https://openstax.org/books/introductory-business-statistics/pages/2-1-display-data#M01_Ch02_tbl010\" style=\"color:blue; text-decoration:underline\"><span style=\"color:#027eb5\">Table 2.8</span></a>&nbsp;shows three age groups, the number of users in each age group, and the proportion (%) of users in each age group. Construct a bar graph using this data.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><strong><span style=\"font-size:14px\">Table2.8</span></strong></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Age groups</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Number of Facebook users</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:20px; vertical-align:bottom; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Proportion (%) of Facebook users</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">13&ndash;25</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">65,082,280</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">45%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">26&ndash;44</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">53,300,200</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">36%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:9px; width:109px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">45&ndash;64</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">27,885,100</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">19%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"color:#000000\"><strong><span style=\"font-size:11pt\"><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238225761623822576.jpg\" style=\"height:597px; width:800px\" /></span></strong></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><strong><span style=\"color:#002060\">EXAMPLE&nbsp;2.6</span></strong></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">The columns in&nbsp;</span><a href=\"https://openstax.org/books/statistics/pages/2-1-stem-and-leaf-graphs-stemplots-line-graphs-and-bar-graphs#M01_Ch02_tbl012\" style=\"color:blue; text-decoration:underline\"><span style=\"color:black\">Table 2.11</span></a><span style=\"color:black\">&nbsp;contain the race or ethnicity of students in U.S. public schools for the class of 2011, percentages for the Advanced Placement (AP) examinee population for that class, and percentages for the overall student population. Create a bar graph with the student race or ethnicity (qualitative data) on the&nbsp;<em>x</em>-axis and the AP examinee population percentages on the&nbsp;<em>y</em>-axis.</span></span></p>\n\n<p>&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><strong><span style=\"font-size:14px\">Table2.11</span></strong></p>\n	</caption>\n	<thead>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:156px\">\n			<div><span style=\"font-size:14px\"><strong>Race/Ethnicity</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom; width:171px\">\n			<div><span style=\"font-size:14px\"><strong>AP Examinee Population</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom\">\n			<div><span style=\"font-size:14px\"><strong>Overall Student Population</strong></span></div>\n			</td>\n		</tr>\n	</thead>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div><span style=\"font-size:14px\">1 = AP</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div><span style=\"font-size:14px\">10.3%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div><span style=\"font-size:14px\">5.7%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div><span style=\"font-size:14px\">2 = Maharashtra</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div><span style=\"font-size:14px\">9.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div><span style=\"font-size:14px\">14.7%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div><span style=\"font-size:14px\">3 = MP</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div><span style=\"font-size:14px\">17.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div><span style=\"font-size:14px\">17.6%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div><span style=\"font-size:14px\">4 = Orissa</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div><span style=\"font-size:14px\">0.6%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div><span style=\"font-size:14px\">1.1%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div><span style=\"font-size:14px\">5 = TN</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div><span style=\"font-size:14px\">57.1%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div><span style=\"font-size:14px\">59.2%</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; width:156px\">\n			<div><span style=\"font-size:14px\">6 = Rajasthan</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px\">\n			<div><span style=\"font-size:14px\">6.0%</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none\">\n			<div><span style=\"font-size:14px\">1.7%</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p><img alt=\"\" src=\"https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238227451623822745.jpg\" style=\"height:559px; width:800px\" /></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"color:#000000\"><span style=\"font-size:14px\"><strong>EXAMPLE&nbsp;2.7</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Below is a two-way table showing the types of pets owned by men and women:</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<table cellspacing=\"0\" class=\"Table\" style=\"border-collapse:collapse; border:none; width:900px\">\n	<caption>\n	<p><strong><span style=\"font-size:14px\">Table2.12</span></strong></p>\n	</caption>\n	<tbody>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\">&nbsp;</div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Dogs</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Cats</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Fish</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Total</strong></span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Men</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">8</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Women</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">6</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">2</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">12</span></div>\n			</td>\n		</tr>\n		<tr>\n			<td style=\"border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\"><strong>Total</strong></span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">8</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">4</span></div>\n			</td>\n			<td style=\"border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px\">\n			<div style=\"text-align:center\"><span style=\"font-size:14px\">20</span></div>\n			</td>\n		</tr>\n	</tbody>\n</table>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Given these data, calculate the conditional distributions for the subpopulation of men who own each pet type</span><span style=\"color:#424242\">.</span></span></p>\n\n<p>&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"color:#000000\"><span style=\"font-size:14px\"><strong>Solution&nbsp;1</strong></span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Men who own dogs = 4/8 = 0.5</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Men who own cats = 2/8 = 0.25</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Men who own fish = 2/8 = 0.25</span></span></p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"color:black\">Note: The sum of all of the conditional distributions must equal one. In this case, 0.5 + 0.25 + 0.25 = 1; therefore, the solution &quot;checks&quot;.</span></span></p>','','1','2.1.5',NULL,'1','2','1','1','1','2021-06-16 05:58:01','2021-06-16 11:28:01'),(2217,97,'2.2 Histograms','','single','html','<p style=\"text-align:justify\"><span style=\"font-size:14px\">For most of the work you do in this book, you will use a histogram to display the data. One advantage of a histogram is that it can readily display large data sets. A rule of thumb is to use a histogram when the data set consists of 100 values or more.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">A&nbsp;<strong>histogram</strong>&nbsp;consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents (for instance, distance from your home to school). The vertical axis is labeled either&nbsp;<strong>frequency</strong>&nbsp;or&nbsp;<strong>relative frequency</strong>&nbsp;(or percent frequency or probability). The graph will have the same shape with either label. The histogram (like the stemplot) can give you the shape of the data, the center, and the spread of the data.</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">The relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample. (Remember, frequency is defined as the number of times an answer occurs.) If:</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<ul>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><em>f</em>&nbsp;= frequency</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><em>n</em>&nbsp;= total number of data values (or the sum of the individual frequencies), and</span></p>\n	</li>\n	<li>\n	<p style=\"text-align:justify\"><span style=\"font-size:14px\"><em>RF</em>&nbsp;= relative frequency,</span></p>\n	</li>\n</ul>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">then:</span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span class=\"math-tex\">\\(RF=\\frac{f}{n}\\)</span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\">For example, if three students in Mr. Ahab&#39;s English class of 40 students received from 90%&nbsp;<span style=\"color:black\">to 100%, then,&nbsp;<em>f</em>&nbsp;= 3,&nbsp;<em>n</em>&nbsp;= 40, and&nbsp;&nbsp;</span><span class=\"math-tex\">\\(RF=\\frac{f}{n}=\\frac{3}{10}=0.075\\)</span>&nbsp;<span style=\"background-color:white\"><span style=\"color:black\">. 7.5% of the students received 90&ndash;100%. 90&ndash;100% are quantitative measures.</span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><strong><span style=\"color:black\">To construct a histogram</span></strong><span style=\"color:black\">, first decide how many&nbsp;<strong>bars</strong>&nbsp;or&nbsp;<strong>intervals</strong>, also called classes, represent the data. Many histograms consist of five to 15 bars or classes for clarity. The number of bars needs to be chosen. Choose a starting point for the first interval to be less than the smallest data value. A&nbsp;<strong>convenient starting point</strong>&nbsp;is a lower value carried out to one more decimal place than the value with the most decimal places. </span></span></span></p>\n\n<p style=\"text-align:justify\">&nbsp;</p>\n\n<p style=\"text-align:justify\"><span style=\"font-size:14px\"><span style=\"background-color:white\"><span style=\"color:black\">For example, if the value with the most decimal places is 6.1 and this is the smallest value, a convenient starting point is 6.05 (6.1 &ndash; 0.05 = 6.05). We say that 6.05 has more precision. If the value with the most decimal places is 2.23 and the lowest value is 1.5, a convenient starting point is 1.495 (1.5 &ndash; 0.005 = 1.495). If the value with the most decimal places is 3.234 and the lowest value is 1.0, a convenient starting point is 0.9995 (1.0 &ndash; 0.0005 = 0.9995). If all the data happen to be integers and the smallest value is two, then a convenient starting point is 1.5 (2 &ndash; 0.5 = 1.5). Also, when the starting point and other boundaries are carried to one additional decimal place, no data value will fall on a boundary. The next two examples go into detail about how to construct a histogram using continuous data and how to create a histogram using discrete data.</span></span></span></p>','','1','2.2',NULL,'1','2','1','0','1','2021-06-21 11:03:28','2021-06-21 16:33:28'),