<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>

<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" summary="Table 1.4 Ethnicity of Students at De Anza College Fall Term 2007 (Census Day) ">
	<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:30px; vertical-align:bottom">
			<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:30px; vertical-align:bottom">
			<div style="text-align:center"><span style="font-size:24px"><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:30px; vertical-align:bottom">
			<div style="text-align:center"><span style="font-size:24px"><strong>Percent</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:29px">
			<div style="text-align:center"><span style="font-size:24px">AP</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<div style="text-align:center"><span style="font-size:24px">8,794</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<div style="text-align:center"><span style="font-size:24px">36.1%</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; height:30px">
			<div style="text-align:center"><span style="font-size:24px">Maharastra</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px">
			<div style="text-align:center"><span style="font-size:24px">1,412</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px">
			<div style="text-align:center"><span style="font-size:24px">5.8%</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:29px">
			<div style="text-align:center"><span style="font-size:24px">Gujarat</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<div style="text-align:center"><span style="font-size:24px">1,298</span></div>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<div style="text-align:center"><span style="font-size:24px">5.3%</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:30px">
			<p style="text-align:center"><span style="font-size:24px">MP</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px">
			<p style="text-align:center"><span style="font-size:24px">4,180</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px">
			<p style="text-align:center"><span style="font-size:24px">17.1%</span></p>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">Orissa</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">146</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">0.6%</span></p>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:30px">
			<p style="text-align:center"><span style="font-size:24px">TN</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px">
			<p style="text-align:center"><span style="font-size:24px">236</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:30px">
			<p style="text-align:center"><span style="font-size:24px">1.0%</span></p>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">Rajasthan</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">5,978</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">24.5%</span></p>
			</td>
		</tr>
		<tr>
			<td style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">TOTAL</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">22,044 out of 24,382</span></p>
			</td>
			<td style="border-bottom:1px solid black; border-left:none; border-right:1px solid black; border-top:none; height:29px">
			<p style="text-align:center"><span style="font-size:24px">90.4% out of 100%</span></p>
			</td>
		</tr>
	</tbody>
</table>

<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>

<p>&nbsp;</p>

<p>&nbsp;</p>

<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>

<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>

<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:#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>

<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:#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>

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

<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>

<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>

<p>&nbsp;</p>

<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>

<p>&nbsp;</p>

<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>

<p>&nbsp;</p>

<p style="text-align:justify"><span style="font-size:16px"><span style="color:#000000"><strong>Pie Charts: No Missing Data</strong></span></span></p>

<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>

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

<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>

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

<p style="text-align:center"><span style="font-size:16px"><span style="color:#000000"><strong>Figure 1.11</strong></span></span></p>

<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>

<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>

<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/16234747361623474736.png" style="height:305px; width:800px" /></span></p>

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

<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>

<p>&nbsp;</p>

<p>&nbsp;</p>

<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>

<p>&nbsp;</p>

<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>

<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/16234747931623474793.png" style="height:272px; width:800px" /></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">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>