<p style="text-align:justify"><span style="font-size:14px"><strong><span style="color:#002060">Example 2.32</span></strong></span></p>

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

<p style="text-align:justify"><span style="font-size:14px">Statistics are used to compare and sometimes identify authors. The following lists show a simple random sample <span style="color:black">that compares the letter counts for three authors.</span></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Terry: 7, 9, 3, 3, 3, 4, 1, 3, 2, 2</span></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Davis: 3, 3, 3, 4, 1, 4, 3, 2, 3, 1</span></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">Maris: 2, 3, 4, 4, 4, 6, 6, 6, 8, 3</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. Make a dot plot for the three authors and compare the shapes.</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. Calculate the mean for each.</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. Calculate the median for each.</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. Describe any pattern you notice between the shape and the measures of center.</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 2.32</strong></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><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238379651623837965.png" style="height:238px; width:800px" /></strong></span></span></p>

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

<p><span style="font-size:14px"><strong><span style="color:#26397f">Figure 2.21 </span></strong><span style="color:black">Terry&rsquo;s distribution has a right (positive) skew.</span></span></p>

<p>&nbsp;</p>

<p>&nbsp;</p>

<p><span style="font-size:14px"><span style="color:black"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238379961623837996.png" style="height:196px; width:800px" /></span></span></p>

<p>&nbsp;</p>

<p><span style="font-size:14px"><strong><span style="color:#26397f">Figure 2.22 </span></strong><span style="color:black">Davis&rsquo;s distribution has a left (negative) skew.</span></span></p>

<p>&nbsp;</p>

<p>&nbsp;</p>

<p><span style="font-size:14px"><span style="color:black"><img alt="" src="https://edupmquestionhelp.s3.ap-south-1.amazonaws.com/hint/uploads/images/16238380311623838031.png" style="height:209px; width:800px" /></span></span></p>

<p>&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><strong><span style="color:#000000">Figure 2.23 Maris&rsquo;s distribution is symmetrically shaped.</span></strong></span></p>

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

<p style="text-align:justify"><span style="font-size:14px"><span style="color:black">b. Terry&rsquo;s mean is 3.7, Davis&rsquo;s mean is 2.7, and Maris&rsquo;s mean is 4.6.</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. Terry&rsquo;s median is 3, Davis&rsquo;s median is 3, and Maris&rsquo;s median is four. It would be helpful to manually calculate these descriptive statistics, using the given data sets and then compare to the graphs.</span> d. It appears that the median is always closest to the high point (the mode), while the mean tends to be farther out on the tail. In a symmetrical distribution, the mean and the median are both centrally located close to the high point of the distribution.</span></p>

<p style="text-align:justify">&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/16238380691623838069.png" style="height:445px; width:800px" /></span></p>

<p>&nbsp;</p>

<p><span style="font-size:14px"><strong>Figure2.25</strong></span></p>