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158 lines
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HTML
158 lines
7.3 KiB
HTML
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<title>Outliers</title>
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<meta name="description" content="Outliers are values that lie outside the other values" />
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<h1 class="center">Outliers</h1>
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<div class="words"><p>
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"Outliers" are values that "<b>lie</b> <b>out</b>side" the other values. </div>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/outlier.svg" alt="outlier" /></p>
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<p>When we collect data, sometimes there are values that are "far away" from the main group of data ... what do we do with them?</p>
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<div style="clear:both"></div>
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<p> </p>
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<div class="example">
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<h3>Example: Long Jump</h3>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/long-jump.jpg" width="150" height="114" alt="long jump" /></p>
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<p>A new coach has been working with the Long Jump team this month, and the athletes' performance has changed. </p>
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<p>Augustus can now jump 0.15m further, June and Carol can jump 0.06m further. </p>
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<p>Here are all the results:</p>
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<ul>
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<li>Augustus: +0.15m</li>
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<li>Tom: +0.11m</li>
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<li>June: +0.06m</li>
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<li>Carol: +0.06m </li>
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<li>Bob: + 0.12m</li>
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<li>Sam: -0.56m</li>
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</ul>
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<p>Oh no! Sam got worse.</p>
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<p>Here are the results on the number line:</p>
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<p class="center"><img src="images/outlier-example1.svg" style="max-width:100%" alt="outlier example 1" /></p>
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<p>The <b><a href="../mean.html">mean</a></b> is: </p>
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<p class="center">(0.15+0.11+0.06+0.06+0.12-0.56) / 6 = -0.06 / 6 = <b>-0.01m</b></p>
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<p>So, on average the performance went <b>DOWN</b>. </p>
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<p class="center"><b>The coach is obviously useless ... right?</b></p>
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</div>
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<p>Sam's result is an "Outlier" ... what if we remove Sam's result?</p>
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<p class="center"><img src="images/out-liar.svg" style="max-width:100%" alt="out, liar!" /></p>
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<div class="example">
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<h3>Example: Long Jump (continued)</h3>
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<p>Let us try the results WITHOUT Sam:</p>
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<p class="center"><img src="images/outlier-example1a.svg" style="max-width:100%" alt="outlier example without outlier" /></p>
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<p class="center">Mean = (0.15+0.11+0.06+0.06+0.12)/5 = <b>0.1 m</b></p>
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<p>Hey, the coach looks much better now!</p>
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</div>
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<p>But is that fair? Can we just get rid of values we don't like?</p>
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<h2>What To Do? </h2>
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<p class="center larger">You need to think "why is that value over there?" </p>
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<p>It may be quite normal to have high or low values</p>
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<ul>
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<li>People can be short or tall</li>
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<li>Some days there is no rain, other days there can be a downpour</li>
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<li>Athletes can perform better or worse on different days</li>
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</ul>
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<p>Or there may be an unusual reason for extreme data</p>
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<div class="example">
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<h3>Example: Long Jump (continued)</h3>
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<p>We find out that Sam was feeling sick that day. Not the coach's fault at all.</p>
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<p>So it is a good idea <b>in this case</b> to remove Sam's result. </p>
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</div>
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<p>When we remove outliers we are <b>changing the data</b>, it is no longer "pure", so we shouldn't just get rid of the outliers without a good reason!</p>
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<p>And when we do get rid of them, we should <b>explain what we are doing and why</b>.</p>
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<h2>Mean, Median and Mode</h2>
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<p>We saw how outliers affect the <a href="../mean.html">mean</a>, but what about the <a href="../median.html">median</a> or <a href="../mode.html">mode</a>?</p>
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<div class="example">
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<h3>Example: Long Jump (continued)</h3>
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<p>The median ("middle" value):</p>
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<ul>
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<li>including Sam is: 0.085</li>
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<li>without Sam is: 0.11 (went up a little)</li>
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</ul>
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<p>The mode (the most common value):</p>
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<ul>
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<li>including Sam is: 0.06</li>
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<li>without Sam is: 0.06 (stayed the same) </li>
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</ul>
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<p>The mode and median didn't change very much.</p>
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<p>They also stayed around where most of the data is. </p>
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</div>
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<p>So it seems that outliers have the biggest effect on the mean, and not so much on the median or mode.</p>
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<p>Hint: calculate the median and mode when you have outliers. </p>
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<p>You can also try the <a href="../numbers/geometric-mean.html">Geometric Mean</a> and <a href="../numbers/harmonic-mean.html">Harmonic Mean</a>.</p>
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<p> </p>
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<script type="text/javascript">getQ(3076, 3077, 3078, 3806, 3807, 3808, 3809, 8773, 8774, 3079);</script>
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<a href="index.html">Data Index</a>
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