Interquartile Range

<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&#39;t actually have to calculate this number. We&#39;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>&nbsp;</p>