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<title>Quartiles</title>
<meta name="Description" content="Quartiles are the values that divide a list of numbers into quarters." />
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<h1 class="center">Quartiles</h1>
<p>Quartiles are the values that divide a list of numbers into quarters:</p>
<ul>
<li>Put the list of numbers <b>in order</b></li>
<li>Then cut the list into<b> four equal parts</b></li>
<li>The Quartiles are at the &quot;cuts&quot; </li>
</ul>
<p>Like this:</p>
<div class="example">
<h3>Example: 5, 7, 4, 4, 6, 2, 8</h3>
<p>Put them in order: 2, 4, 4, 5, 6, 7, 8</p>
<p>Cut the list into quarters:</p>
<p class="center"><img src="images/quartiles-a.svg" alt="Quartiles of 2, 4, 4, 5, 6, 7, 8" /></p>
<p>And the result is:</p>
<ul>
<li>Quartile 1 (Q1) = <b>4</b></li>
<li>Quartile 2 (Q2), which is also the <a href="../median.html">Median</a>, = <b>5</b></li>
<li>Quartile 3 (Q3) = <b>7</b></li>
</ul>
</div>
<p>Sometimes a &quot;cut&quot; is between two numbers ... the Quartile is the average of the two numbers.</p>
<div class="example">
<h3>Example: 1, 3, 3, 4, 5, 6, 6, 7, 8, 8</h3>
<p>The numbers are already in order</p>
<p>Cut the list into quarters:</p>
<p class="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 class="center 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>
<h2>Interquartile Range</h2>
<p> The &quot;Interquartile Range&quot; is from Q1 to Q3:</p>
<div class="center"><img src="images/interquartile-range.svg" alt="Interquartile Range" />
</div>
<p>To calculate it just <b>subtract Quartile 1 from Quartile 3</b>, like this:</p>
<div class="example">
<h3>Example: </h3>
<p class="center"><img src="images/quartiles-a.svg" alt="Quartiles of 2, 4, 4, 5, 6, 7, 8" /></p>
<p>The <b>Interquartile Range</b> is:</p>
<p class="center large">Q3 &minus; Q1 = 7 &minus; 4 = <b>3</b></p>
</div>
<h2>Box and Whisker Plot</h2>
<p>We can show all the important values in a &quot;Box and Whisker Plot&quot;, like this:</p>
<p class="center"><span class="large"><img src="images/box-whisker-plot.svg" alt="Box and Whisker Plot" /></span></p>
<p>A final example covering everything:</p>
<div class="example">
<h3>Example: <b>Box and Whisker Plot and Interquartile Range</b> for</h3>
<p class="center larger">4, 17, 7, 14, 18, 12, 3, 16, 10, 4, 4, 11
</p>
<p>Put them in order: </p>
<p class="center larger">3, 4, 4, 4, 7, 10, 11, 12, 14, 16, 17, 18</p>
<p>Cut it into quarters: </p>
<p class="center larger"><span class="hilite">3, 4, 4</span> | <span class="hilite">4, 7, 10</span> | <span class="hilite">11, 12, 14</span> | <span class="hilite">16, 17, 18</span></p>
<p>In this case all the quartiles are between numbers:</p>
<ul>
<li>Quartile 1 (Q1) = (4+4)/2 = <b>4</b></li>
<li>Quartile 2 (Q2) = (10+11)/2 = <b>10.5</b></li>
<li>Quartile 3 (Q3) = (14+16)/2 = <b>15</b></li>
</ul>
<p>Also:</p>
<ul>
<li>The Lowest Value is <b>3</b>, </li>
<li>The Highest Value is <b>18</b></li>
</ul>
<p>So now we have enough data for the <b>Box and Whisker Plot</b>:</p>
<p class="center large"><img src="images/box-whisker-plot-ex1.svg" alt="box whisker plot" /></p>
<p>And the <b>Interquartile Range</b> is:</p>
<p class="center large">Q3 &minus; Q1 = 15 &minus; 4 = <b>11</b></p>
</div>
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<a href="../median.html">Median</a>
<a href="index.html">Data Index</a>
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