<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Example 2.24</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The following data are the heights of 40 students in a statistics class:</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">59, 60, 61, 62, 62, 63, 63, 64, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 65, 66, 66, 67, 67, 68, 68, 69, 70, 70, 70, 70,70, 71, 71, 72, 72, 73, 74, 74, 75, 77.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Construct a box plot with the following properties. Calculator instructions for finding the five number summary</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">follow this example:</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">&bull; Minimum value = 59</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">&bull; Maximum value = 77</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">&bull; </span><em><span style="color:black">Q</span></em><span style="color:black">1: First quartile = 64.5</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">&bull; </span><em><span style="color:black">Q</span></em><span style="color:black">2: Second quartile or median = 66</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">&bull; </span><em><span style="color:black">Q</span></em><span style="color:black">3: Third quartile = 70</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238341801623834180.png" style="height:138px; width:800px" /></span></p>

<p style="text-align:center"><span style="font-size:14px"><strong><span style="color:#26397f">Figure 2.14</span></strong></span></p>

<p style="text-align:center">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px">a. Each quarter has approximately 25 percent of the data.</span></p>

<p style="text-align:justify"><span style="font-size:14px">b. The spreads of the four quarters are 64.5 &ndash; 59 = 5.5 (first quarter), 66 &ndash; 64.5 = 1.5 (second quarter), 70 &ndash; 66= 4 (third quarter), and 77 &ndash; 70 = 7 (fourth quarter). So, the second quarter has the smallest spread, and the fourth quarter has the largest spread.</span></p>

<p style="text-align:justify"><span style="font-size:14px">c. Range = maximum value &ndash; minimum value = 77 &ndash; 59 = 18.</span></p>

<p style="text-align:justify"><span style="font-size:14px">d. Interquartile Range: <em>IQR </em>= <em>Q</em>3 &ndash; <em>Q</em>1 = 70 &ndash; 64.5 = 5.5.</span></p>

<p style="text-align:justify"><span style="font-size:14px">e. The interval 59&ndash;65 has more than 25 percent of the data, so it has more data in it than the interval 66&ndash;70, which has 25 percent of the data.</span></p>

<p style="text-align:justify"><span style="font-size:14px">f. The middle 50 percent (middle half) of the data has a range of 5.5 inches.</span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">For some sets of data, some of the largest value, smallest value, first quartile, median, and third quartile may be the same.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">For instance, you might have a data set in which the median and the third quartile are the same. In this case, the diagram would not have a dotted line inside the box displaying the median. The right side of the box would display both the third quartile and the median. For example, if the smallest value and the first quartile were both one, the median and the third quartile were both five, and the largest value was seven, the box plot would look like the following:</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238342221623834222.png" style="height:214px; width:800px" /></span></p>

<p style="text-align:center"><span style="font-size:14px"><strong><span style="color:#26397f">Figure 2.15</span></strong></span></p>

<p style="text-align:center">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">In this case, at least 25 percent of the values are equal to one. Twenty-five percent of the values are between one and five, inclusive. At least 25 percent of the values are equal to five. The top 25 percent of the values fall between five and seven, inclusive.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><strong>Example 2.25</strong></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Test scores for Mr. Ramirez&#39;s class held during the day are as follows:</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">99, 56, 78, 55.5, 32, 90, 80, 81, 56, 59, 45, 77, 84.5, 84, 70, 72, 68, 32, 79, 90.</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Test scores for Ms. Park&#39;s class held during the evening are as follows:</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">98, 78, 68, 83, 81, 89, 88, 76, 65, 45, 98, 90, 80, 84.5, 85, 79, 78, 98, 90, 79, 81, 25.5.</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">a. Find the smallest and largest values, the median, and the first and third quartile for Mr. Ramirez&#39;s class.</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">b. Find the smallest and largest values, the median, and the first and third quartile for Ms. Park&#39;s class.</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">c. For each data set, what percentage of the data is between the smallest value and the first quartile? the first quartile and the median? the median and the third quartile? the third quartile and the largest value? What percentage of the data is between the first quartile and the largest value?</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">d. Create a box plot for each set of data. Use one number line for both box plots.</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">e. Which box plot has the widest spread for the middle 50 percent of the data, the data between the first and third quartiles? What does this mean for that set of data in comparison to the other set of data?</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Solution 2.25</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">a. Min = 32</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">Q</span></em><span style="color:black">1 = 56</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">M </span></em><span style="color:black">= 74.5</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">Q</span></em><span style="color:black">3 = 82.5</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Max = 99</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">b. Min = 25.5</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">Q</span></em><span style="color:black">1 = 78</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">M </span></em><span style="color:black">= 81</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">Q</span></em><span style="color:black">3 = 89</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Max = 98</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">c. Mr. Ramirez&#39;s class: There are six data values ranging from 32 to 56: 30 percent. There are six data values ranging from 56 to 74.5: 30 percent. There are five data values ranging from 74.5 to 82.5: 25 percent. There are five data values ranging from 82.5 to 99: 25 percent. There are 16 data values between the first quartile, 56, and the largest value, 99: 75 percent. Ms. Park&rsquo;s class: There are six data values ranging from 25.5 to 78: 27 percent. There are five data values ranging from 78 to the first instance of 81: 23 percent. There are six data values ranging from the second instance of 81 to 89: 27 percent. There are five data values ranging from 90 to 98: 23 percent. There are 17 values between the first quartile, 78, and the largest value, 98: 77 percent.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238342921623834292.png" style="height:296px; width:800px" /></span></span></p>

<p style="text-align:center"><span style="font-size:14px"><span style="color:#000000"><strong>&nbsp;Figure 2.16</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">d.</span><strong> &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; </strong></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">e. The first data set has the wider spread for the middle 50 percent of the data. The </span><em><span style="color:black">IQR </span></em><span style="color:black">for the first data set is greater than the </span><em><span style="color:black">IQR </span></em><span style="color:black">for the second set. This means that there is more variability in the middle 50 percent of the first data se</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Example 2.26</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Graph a box-and-whisker plot for the following data values shown:</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">10, 10, 10, 15, 35, 75, 90, 95, 100, 175, 420, 490, 515, 515, 790</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The five numbers used to create a box-and-whisker plot are as follows:</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Min: 10</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">Q</span></em><span style="color:black">1: 15</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Med: 95</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><em><span style="color:black">Q</span></em><span style="color:black">3: 490</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Max: 790</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">The following graph shows the box-and-whisker plot.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238345621623834562.png" style="height:158px; width:800px" /></span></p>

<p style="text-align:center"><span style="font-size:14px"><span style="color:#000000"><strong>Figure 2.17</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<h2 style="text-align:justify">&nbsp;</h2>