<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>EXAMPLE&nbsp;2.5</strong></span></span></p>

<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>

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

<table cellspacing="0" class="Table" style="border-collapse:collapse; border:none; width:900px">
	<caption>
	<p><span style="font-size:14px"><strong>Table2.8</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:20px; vertical-align:bottom; width:109px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Age groups</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:20px; vertical-align:bottom; width:212px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Number of Facebook users</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:20px; vertical-align:bottom; width:272px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Proportion (%) of Facebook users</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:9px; width:109px">
			<div style="text-align:center"><span style="font-size:14px">13&ndash;25</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px">
			<div style="text-align:center"><span style="font-size:14px">65,082,280</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px">
			<div style="text-align:center"><span style="font-size:14px">45%</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:9px; width:109px">
			<div style="text-align:center"><span style="font-size:14px">26&ndash;44</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px">
			<div style="text-align:center"><span style="font-size:14px">53,300,200</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px">
			<div style="text-align:center"><span style="font-size:14px">36%</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:9px; width:109px">
			<div style="text-align:center"><span style="font-size:14px">45&ndash;64</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:212px">
			<div style="text-align:center"><span style="font-size:14px">27,885,100</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:9px; width:272px">
			<div style="text-align:center"><span style="font-size:14px">19%</span></div>
			</td>
		</tr>
	</tbody>
</table>

<p>&nbsp;</p>

<p><span style="font-size:14px"><span style="color:#333333">Solution&nbsp;1</span></span></p>

<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>

<p style="text-align:center"><span style="font-size:14px"><strong><span style="color:#424242">Figure&nbsp;2.3</span></strong></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><strong><span style="color:#002060">EXAMPLE&nbsp;2.6</span></strong></span></p>

<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>

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

<table cellspacing="0" class="Table" style="border-collapse:collapse; border:none; width:900px">
	<caption>
	<div><span style="font-size:14px"><strong>Table2.11</strong></span></div>
	</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; vertical-align:bottom; width:156px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Race/Ethnicity</strong></span></div>
			</td>
			<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">
			<div style="text-align:center"><span style="font-size:14px"><strong>AP Examinee Population</strong></span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; vertical-align:bottom">
			<div style="text-align:center"><span style="font-size:14px"><strong>Overall Student Population</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; width:156px">
			<div style="text-align:center"><span style="font-size:14px">1 = AP</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px">
			<div style="text-align:center"><span style="font-size:14px">10.3%</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none">
			<div style="text-align:center"><span style="font-size:14px">5.7%</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; width:156px">
			<div style="text-align:center"><span style="font-size:14px">2 = Maharashtra</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px">
			<div style="text-align:center"><span style="font-size:14px">9.0%</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none">
			<div style="text-align:center"><span style="font-size:14px">14.7%</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; width:156px">
			<div style="text-align:center"><span style="font-size:14px">3 = MP</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px">
			<div style="text-align:center"><span style="font-size:14px">17.0%</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none">
			<div style="text-align:center"><span style="font-size:14px">17.6%</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; width:156px">
			<div style="text-align:center"><span style="font-size:14px">4 = Orissa</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px">
			<div style="text-align:center"><span style="font-size:14px">0.6%</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none">
			<div style="text-align:center"><span style="font-size:14px">1.1%</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; width:156px">
			<div style="text-align:center"><span style="font-size:14px">5 = TN</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px">
			<div style="text-align:center"><span style="font-size:14px">57.1%</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none">
			<div style="text-align:center"><span style="font-size:14px">59.2%</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; width:156px">
			<div style="text-align:center"><span style="font-size:14px">6 = Rajasthan</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; width:171px">
			<div style="text-align:center"><span style="font-size:14px">6.0%</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none">
			<div style="text-align:center"><span style="font-size:14px">1.7%</span></div>
			</td>
		</tr>
	</tbody>
</table>

<p>&nbsp;</p>

<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>

<p style="text-align:justify"><span style="font-size:14px"><strong>EXAMPLE&nbsp;<span style="color:#2f5496">2.7</span></strong></span></p>

<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>

<table cellspacing="0" class="Table" style="border-collapse:collapse; border:none; width:900px">
	<caption>
	<div><span style="font-size:14px"><strong>Table2.12</strong></span></div>
	</caption>
	<tbody>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; height:11px">
			<div style="text-align:center">&nbsp;</div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:1px solid black; height:11px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Dogs</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:11px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Cats</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:11px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Fish</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:11px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Total</strong></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:11px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Men</strong></span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">4</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">2</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">2</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">8</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:11px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Women</strong></span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">4</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">6</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">2</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">12</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:11px">
			<div style="text-align:center"><span style="font-size:14px"><strong>Total</strong></span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">8</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">8</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">4</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:11px">
			<div style="text-align:center"><span style="font-size:14px">20</span></div>
			</td>
		</tr>
	</tbody>
</table>

<p>&nbsp;</p>

<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>

<p><span style="font-size:14px"><strong><span style="color:#4472c4">Solution&nbsp;1</span></strong></span></p>

<p><span style="font-size:14px"><span style="color:black">Men who own dogs = 4/8 = 0.5</span></span></p>

<p><span style="font-size:14px"><span style="color:black">Men who own cats = 2/8 = 0.25</span></span></p>

<p><span style="font-size:14px"><span style="color:black">Men who own fish = 2/8 = 0.25</span></span></p>

<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>