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144 lines
5.3 KiB
HTML
144 lines
5.3 KiB
HTML
<!DOCTYPE html>
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<article id="content" role="main">
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<h1 class="center">Skewed Data</h1>
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<p>Data can be "skewed", meaning it tends to have a <b>long tail</b> on one side or the other:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="images/normal-distribution-skew-left.svg" alt="data skewed left" height="177" width="202"></td>
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<td> </td>
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<td><img src="images/normal-distribution.svg" alt="data no skew" height="165" width="223"></td>
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<td> </td>
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<td><img src="images/normal-distribution-skew-right.svg" alt="data skewed right" height="177" width="202"></td>
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</tr>
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<tr>
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<td style="text-align:left;">Negative Skew</td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;">No Skew</td>
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<td style="text-align:center;"> </td>
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<td style="text-align:right;">Positive Skew</td>
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</tr>
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</tbody></table>
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<h2>Negative Skew?</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/skewed-distribution-negative.svg" alt="skewed distribution negative" height="211" width="279"></p>
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<p>Why is it called <b>negative</b> skew? Because the long "tail" is on the negative side of the peak.</p>
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<p>Some people say it is "skewed to the left" (the long tail is on the left hand side)</p>
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<p>The mean is also on the left of the peak.</p>
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<div style="clear:both">
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</div>
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<h2>The Normal Distribution has No Skew</h2>
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<p class="center"><img src="images/normal-distribution-2.svg" alt="normal distribution with mean median mode at center" height="162" width="299"><br>
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A <a href="standard-normal-distribution.html">Normal Distribution</a> is not skewed.<br>
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It is perfectly symmetrical.<br>
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And the Mean is exactly at the peak.</p>
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<h2>Positive Skew</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/skewed-distribution.svg" alt="skewed distribution" height="211" width="279"></p>
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<p>And<b> positive</b> skew is when the long tail is on the positive side of the peak</p>
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<p>Some people say it is "skewed to the right".</p>
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<p>The mean is on the right of the peak value.</p>
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<div style="clear:both">
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</div>
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<p> </p>
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<h2>Example: Income Distribution</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/income-distribution1.svg" alt="income distribution" height="240" width="374"></p><p>Here is some data extracted from a recent Census.</p>
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<p>As you can see it is <b>positively skewed</b> ... in fact the tail continues way past $100,000</p>
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<div style="clear:both">
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</div>
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<h2>Calculating Skewness</h2>
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<p>"Skewness" (the amount of skew) can be calculated, for example you could use the SKEW() function in Excel or OpenOffice Calc.</p>
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<p> </p>
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<div class="questions">8775, 8776, 8777, 8778, 8779, 8780, 8781, 8782, 8783, 8784</div>
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<div class="related">
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<a href="standard-normal-distribution.html">Normal Distribution</a>
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<a href="index.html">Data Index</a>
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</div>
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