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186 lines
6.1 KiB
HTML
186 lines
6.1 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/activity/averages-brain-teaser.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:41:49 GMT -->
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<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Activity: Averages Brain-Teaser</title>
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<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<link rel="preload" href="../main4.js" as="script">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: Averages Brain-Teaser</h1>
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<p>Here is a little puzzle about <a href="../mean.html">averages</a>. Is it right?</p>
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<p> </p>
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<div class="example">
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<h3>Who is Better at Kicking Goals?</h3>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../images/soccer-teams.jpg" alt="soccer teams" height="86" width="209"></p>
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<p>At practice last week:</p>
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<ul>
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<li>You scored 2 of 10 shots at goal</li>
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<li>Sam scored 3 of 10 shots</li>
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</ul>
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<p>Sam is better!</p>
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<p> </p>
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<p>This week:</p>
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<ul>
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<li>You scored 53 of 100 shots</li>
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<li>Sam scored 6 of 10 shots</li>
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</ul>
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<p>Sam is still better.</p>
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<p> </p>
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<p>But let's <b>add up the scores for BOTH weeks</b>:</p>
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<ul>
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<li>You scored 55 of 110 shots: that is 50%</li>
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<li>Sam scored 9 of 20 shots: that is only 45%</li>
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</ul>
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<p>Hang on! YOU are better!</p>
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<p> </p>
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<p>Sam was better last week and this week ... but you are better over both weeks?</p>
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</div>
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<p>Please explain.</p>
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<p> </p>
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<p>...</p>
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<p> </p>
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<p>Make a table with all the data and do the calculations yourself</p>
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<table align="center" cellspacing="0" cellpadding="4" border="1">
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<tbody>
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<tr>
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<td style="text-align:right;"> </td>
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<td align="center" width="200">Sam</td>
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<td align="center" width="200">You</td>
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</tr>
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<tr>
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<td align="right" height="60">Last Week</td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td align="right" height="60">This Week</td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td align="right" height="60"><b>Both Weeks</b></td>
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<td> </td>
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<td> </td>
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</tr>
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</tbody></table>
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<p> </p>
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<p>....</p>
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<p> </p>
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<p> </p>
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<p><b>... read on after you have thought about it ...</b></p>
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<p> </p>
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<p> </p>
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<p>...</p>
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<p> </p>
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<p> </p>
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<p> </p>
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<div class="example">
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<h3>It is All True</h3>
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<p> </p>
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<p>Because you had SO MANY shots at goal this week, and did well at them, you lifted your two-week average above Sam's.</p>
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<p> </p>
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<p>At practice last week:</p>
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<ul>
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<li>You scored 2 of 10 (<b>20%</b>)</li>
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<li>Sam scored 3 of 10 (<b>30%</b>)</li>
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</ul>
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<p>This week:</p>
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<ul>
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<li><span class="hilite">You scored 53 of 100 (<b>53%</b>)</span></li>
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<li>Sam scored 6 of 10 (<b>60%</b>)</li>
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</ul>
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<p> </p>
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<p>For BOTH weeks:</p>
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<ul>
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<li>You scored 55 of 110 (<b>50%</b>)</li>
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<li>Sam scored 9 of 20 (<b>45%</b>)</li>
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</ul>
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<p> </p>
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</div>
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<p> </p>
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<p>To be fair, we should really compare the averages when your and Sam's attempts at goal is roughly the same.</p>
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<p>If Sam had attempted 100 shots this week, he may have scored 60 out of 100, and his two-week average would have been about <b>57%</b>, better than you.</p>
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<p>So be careful when comparing two sets of data with widely different counts.</p>
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<p class="info"> This is an example of "Simpson's paradox" if you want to find out more.</p>
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<p><i><br></i></p>
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<p><i>Note: only certain sets of data produce this "paradox", usually everything makes sense.</i></p>
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<p> </p>
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<div class="related">
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<a href="../data/index.html">Data Index</a>
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</div>
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<!-- #EndEditable -->
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</article>
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<div id="adend" class="centerfull noprint"></div>
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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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