<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-interquartile-range" target="_blank">Interquartile Range Exercise</a></p><p>In a previous mountain entry, we learned how to calculate the $Q_1$, $Q_2$, and $Q_3$ values.</p>
<p>Two of those values can be used to calculate the <strong><span style="color:#8e44ad;">Interquartile Range</span></strong>.</p>
<p><strong><span style="color:#e74c3c;">The Formula</span></strong></p>
<p>$$interquartile \ range = Q_3 - Q_1$$</p>
<p><strong><span style="color:#27ae60;">Example</span></strong></p>
<p><em>Calculate the interquartile range of the dataset below:</em></p>
<p>$$9, 13, 17, 30, 34, 37, 42, 46, 49, 53$$</p>
<p style="margin-left: 40px;"><strong><u>Step 1</u></strong>: Calculate the $Q_2$ value (the median) and draw a vertical line through it. This divides the dataset into two equal halves.</p>
<p>$$median = \frac{34+37}{2} = 35.5$$</p>
<p style="margin-left: 80px;"><strong><span style="color:#e74c3c;">Note</span></strong>: You don't actually have to calculate this number. We're just trying to find the location in the dataset where we put that vertical line to divide it into two equal halves.</p>
<p style="margin-left: 40px;"><strong><u>Step 2</u></strong>: Find the $Q_1$ value (the median of the first half): $9, 13, 17, 30, 34$</p>
<p>$$Q_1 = 17$$</p>
<p style="margin-left: 40px;"><strong><u>Step 3</u></strong>: Find the $Q_3$ value (the median of the second half): $37, 42, 46, 49, 53$</p>
<p>$$Q_3 = 46$$</p>
<p style="margin-left: 40px;"><strong><u>Step 4</u></strong>: Bring it home.</p>
<p><span style="color:#27ae60;">$$interquartile \ range = Q_3 - Q_1 = 46-17 = 29$$</span></p>
<p> </p>