<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>

<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>

<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>

<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>

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

<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 ">
	<caption>
	<p><span style="font-size:14px">Table1.5&nbsp;Frequency Table of Student Work Hours</span></p>
	</caption>
	<thead>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><strong><span style="color:#424242">Data value</span></strong></span></div>
			</td>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><strong><span style="color:#424242">Frequency</span></strong></span></div>
			</td>
		</tr>
	</thead>
	<tbody>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">2</span></span></div>
			</td>
			<td style="background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">3</span></span></div>
			</td>
		</tr>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">3</span></span></div>
			</td>
			<td style="background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">5</span></span></div>
			</td>
		</tr>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">4</span></span></div>
			</td>
			<td style="background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">3</span></span></div>
			</td>
		</tr>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">5</span></span></div>
			</td>
			<td style="background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">6</span></span></div>
			</td>
		</tr>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">6</span></span></div>
			</td>
			<td style="background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">2</span></span></div>
			</td>
		</tr>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">7</span></span></div>
			</td>
			<td style="background-color:white; border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:38%">
			<div style="text-align:center"><span style="font-size:28px"><span style="color:#424242">1</span></span></div>
			</td>
		</tr>
	</tbody>
</table>

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

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

<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>

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

<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>

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

<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>

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

<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>

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

<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>

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

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

<table cellspacing="0" class="Table" style="border-collapse:collapse; border:none; width:900px">
	<caption>
	<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>
	</caption>
	<thead>
		<tr>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><strong>Data value</strong></span></div>
			</td>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><strong>Frequency</strong></span></div>
			</td>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><strong>Relative frequency</strong></span></div>
			</td>
			<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%">
			<div style="text-align:center"><span style="font-size:28px"><strong>Cumulative relative frequency</strong></span></div>
			</td>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">2</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">3</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%">
			<div style="text-align:center"><span style="font-size:28px"><em><span class="math-tex">\(\frac{3}{20}\)</span></em> or .15</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%">
			<div style="text-align:center"><span style="font-size:28px">0.15</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">3</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">5</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%">
			<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>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%">
			<div style="text-align:center"><span style="font-size:28px">0.15 + 0.25 = 0.40</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">4</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">3</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%">
			<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>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%">
			<div style="text-align:center"><span style="font-size:28px">0.40 + 0.15 = 0.55</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">5</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">6</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%">
			<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>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%">
			<div style="text-align:center"><span style="font-size:28px">0.55 + 0.30 = 0.85</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">6</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">2</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:26%">
			<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>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:34px; width:38%">
			<div style="text-align:center"><span style="font-size:28px">0.85 + 0.10 = 0.95</span></div>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:33px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">7</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:33px; width:17%">
			<div style="text-align:center"><span style="font-size:28px">1</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:33px; width:26%">
			<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>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:33px; width:38%">
			<div style="text-align:center"><span style="font-size:28px">0.95 + 0.05 = 1.00</span></div>
			</td>
		</tr>
	</tbody>
</table>

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

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

<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>

<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>

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

<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>

<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>

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

<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>

<ul>
	<li>
	<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>
	</li>
	<li>
	<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>
	</li>
	<li>
	<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>
	</li>
	<li>
	<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>
	</li>
	<li>
	<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>
	</li>
	<li>
	<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>
	</li>
	<li>
	<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>
	</li>
	<li>
	<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>
	</li>
</ul>

<p style="text-align:justify"><br />
<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>