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<!doctype html>
<html lang="en"><!-- #BeginTemplate "/Templates/Advanced.dwt" --><!-- DW6 -->
<!-- Mirrored from www.mathsisfun.com/data/percentiles.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:41:57 GMT -->
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<!-- #BeginEditable "doctitle" -->
<title>Percentiles</title>
<meta name="description" content="Percentile is the value below which a percentage of data falls." />
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<h1 style="margin-top:5pt;margin-bottom:5pt;text-align:center">Percentiles</h1>
<p class="center larger">Percentile:
the value below which a percentage of data falls. </p>
<div class="example">
<h3> Example:
You are the fourth tallest person in a group of 20</h3>
<p>80% of people are shorter than you:</p>
<p class="center"><img src="images/percentile-80.svg" alt="percentile 80%" /></p>
<p>That means you are at the <b>80th percentile</b>.</p>
<p>If your height is 1.85m then &quot;1.85m&quot; is the 80th percentile height in that group.</p>
</div>
<h2>In Order</h2>
<p>Have the data <b>in order</b>, so you know which values are above and below. </p>
<ul>
<li>To calculate percentiles of height: have the data in height order (sorted by height). </li>
<li> To calculate percentiles of age: have the data in age order. <br>
</li>
<li>And so on.</li>
</ul>
<h2>Grouped Data</h2>
<p>When the data is grouped:</p>
<p class="center">Add up all percentages <b>below</b> the score,<br>
plus <b>half</b> the percentage <b>at</b> the score.</p>
<div class="example">
<h3>Example: You Score a B!</h3>
<p>In the test 12% got D, 50% got C, 30% got B and 8% got A </p>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/percentile-rank.svg" alt="percentile rank 77%" /></p><p>You got a B, so add up</p><ul>
<li>all the 12% that got D, </li>
<li>all the 50% that got C,</li>
<li>half of the 30% that got B, </li>
</ul>
<p>for a total percentile of 12% + 50% + 15% = <b>77% </b></p>
<p>In other words you did &quot;as well or better than 77% of the class&quot; </p>
<p>(Why take half of B? Because you shouldn't imagine you got the &quot;Best B&quot;, or the &quot;Worst B&quot;, just an average B.) </p>
</div>
<h2>Deciles</h2>
<p><b>Deciles</b> are similar to Percentiles (sounds like decimal and percentile together), as they split the data into <b>10% groups</b>:</p>
<ul>
<li>The <b>1st decile</b> is the <b>10th percentile</b> (the value that divides the data so <b>10%</b> is below it)</li>
<li>The <b>2nd decile</b> is the <b>20th percentile</b> (the value that divides the data so <b>20%</b> is below it)</li>
<li>etc!</li>
</ul>
<div class="example">
<h3> Example: (continued)</h3>
<p class="center"><img src="images/percentile-80.svg" alt="percentile 80%" /></p>
<p>You are at the <b>8th decile</b> (the 80th percentile).</p>
</div>
<h2>Quartiles </h2>
<p>Another related idea is <a href="quartiles.html">Quartiles</a>, which splits the data into quarters:</p>
<div class="example">
<h3>Example: 1, 3, 3, 4, 5, 6, 6, 7, 8, 8</h3>
<p>The numbers are in order. Cut the list into quarters:</p>
<p align="center"><img src="images/quartiles-c.svg" alt="Quartiles" /></p>
<p>In this case Quartile 2 is half way between 5 and 6:</p>
<p align="center" class="larger">Q2 = (5+6)/2 = <b>5.5</b></p>
<p>And the result is:</p>
<ul>
<li>Quartile 1 (Q1) = <b>3</b></li>
<li>Quartile 2 (Q2) = <b>5.5</b></li>
<li>Quartile 3 (Q3) = <b>7</b></li>
</ul>
</div>
<p>The Quartiles also divide the data into divisions
of 25%, so:</p>
<ul style="list-style:disc">
<li>Quartile
1 (Q1) can be called the <span style="font-weight:bold">25th percentile</span></li>
<li>Quartile
2 (Q2) can be called the <span style="font-weight:bold">50th percentile</span></li>
<li>Quartile
3 (Q3) can be called the <span style="font-weight:bold">75th percentile</span></li>
</ul>
<div class="example">
<h3>Example: (continued)</h3>
<p>For <b>1, 3, 3, 4, 5, 6, 6, 7, 8, 8</b>:</p>
<ul>
<li>The 25th percentile = <b>3</b></li>
<li>The 50th percentile = <b>5.5</b></li>
<li>The 75th percentile = <b>7</b></li>
</ul>
</div>
<h2>Estimating Percentiles</h2>
<p>We can estimate percentiles from a <a href="line-graphs.html"><span><span style="text-decoration:underline">line graph</span></span></a>.</p>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/shopping.jpg" width="180" height="113" alt="shopping" /></p>
<h3>Example: Shopping</h3>
<p> A total of 10,000 people visited the shopping mall over 12 hours:</p>
<div class="beach">
<table align="center">
<tr valign="top">
<th align="right">Time (hours)</th>
<th width="80" align="right">People</th>
</tr>
<tr valign="top">
<td align="right">0</td>
<td align="right">0</td>
</tr>
<tr valign="top">
<td align="right">2</td>
<td align="right">350</td>
</tr>
<tr valign="top">
<td align="right">4</td>
<td align="right">1100</td>
</tr>
<tr valign="top">
<td align="right">6</td>
<td align="right">2400</td>
</tr>
<tr valign="top">
<td align="right">8</td>
<td align="right">6500</td>
</tr>
<tr valign="top">
<td align="right">10</td>
<td align="right">8850</td>
</tr>
<tr valign="top">
<td align="right">12</td>
<td align="right">10,000</td>
</tr>
</table>
</div>
<h3>a) Estimate
the 30th percentile (when 30% of the visitors had arrived).</h3>
<h3>b) Estimate
what percentile of visitors had
arrived after 11 hours.</h3>
<p>First draw
a line graph of the data: plot the points
and join them with a smooth curve:</p>
<p class="center"><img src="images/percentile-graph.svg" alt="percentile graph" /></p>
<p style="margin-left:0pt;text-align:center">
<center>
</center>
</p>
<p>&nbsp;</p>
<p>a) The 30th
percentile occurs when the visits reach 3,000.</p>
<p>Draw a line
horizontally across from 3,000 until you hit the curve, then draw a
line vertically downwards to read off the time on the horizontal axis:</p>
<p class="center"><img src="images/percentile-graph-30.svg" alt="percentile graph 30% = 6.5" /></p>
<p style="margin-left:0pt;text-align:center">
<center>
</center>
</p>
<p>So the <b>30th
percentile</b> occurs after about <b>6.5 hours</b>.</p>
<p>&nbsp;</p>
<p>b) To estimate
the percentile of visits after 11
hours: draw a line vertically up from 11 until you hit the curve, then
draw a line horizontally across to read off the population on the vertical
axis:</p>
<p class="center"><img src="images/percentile-graph-95.svg" alt="percentile graph 11 = 95%" /></p>
<p style="margin-left:0pt;text-align:center">
<center>
</center>
</p>
<p>So the visits
at <b>11 hours</b> were about 9,500, which is the <b>95th percentile</b>.</p>
</div>
<p>&nbsp;</p>
<div class="questions">
<script>getQ(697, 1470, 3802, 3803, 8649, 8650, 8651, 8652, 8653, 8654);</script>&nbsp;
</div>
<div class="related"><a href="quartiles.html">Quartiles</a><a href="index.html">Data Index</a></div>
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