Quartiles
<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-quartiles" target="_blank">Quartiles Exercise</a></span></p><p>The easiest way to wrap your mind around <strong><span style="color:#8e44ad;">Quartiles</span></strong>, in my opinion, is to think of halves. For example, notice how we can divide a dataset consisting of an even number of items into two halves:</p>
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<p>With Quartiles, we're simply dividing the dataset into four groups.</p>
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<p>As you can probably imagine, things get a bit messy if the number of items in a dataset is not a multiple of $4$. Thankfully, GRE often avoids asking about Quartiles in these cases.</p>
<p><strong><span style="color:#27ae60;">The $Q_1$, $Q_2$, and $Q_3$ Values</span></strong></p>
<p>However, even in the case where the number of items is not a multiple of $4$, we have the following values:</p>
<ul>
<li><strong>$Q_1$</strong>: A boundary number that separates the lowest $25\%$ of values in a dataset.</li>
<li><strong>$Q_2$</strong>: A boundary number that separates the lowest $50\%$ of values in a dataset.
<ul>
<li><strong><span style="color:#e74c3c;">NOTE</span>: </strong>This is the median! Yes, the $Q_2$ value is the median!</li>
</ul>
</li>
<li><strong>$Q_3$</strong>: A boundary number that separates the lowest $75\%$ of values in a dataset.</li>
</ul>
<p><strong><span style="color:#27ae60;">Calculating These Values</span></strong></p>
<p>What are the $Q_1$, $Q_2$, and $Q_3$ values for the three datasets below:</p>
<p style="text-align: center;"><strong><u>Dataset 1</u></strong>: $10, 14, 18, 21, 25, 34, 46$</p>
<p style="text-align: center;"><strong><u>Dataset 2</u></strong>: $13, 17, 19, 22, 23, 40, 41, 46$</p>
<p style="text-align: center;"><strong><u>Dataset 3</u></strong>: $12, 14, 18, 25, 34, 38, 42, 44, 46, 48$</p>
<p><strong><span style="color:#e74c3c;">NOTE</span></strong>: We already know how to calculate $Q_2$. That's the median. See the previous mountain entry if you forgot about that one.</p>
<ul>
<li><strong><span style="color:#27ae60;">Step 1</span></strong>: Find the median (the $Q_2$ value) and draw a vertical line through it. This line separates the dataset into two equal halves.
<ul>
<li>Sometimes the line goes through a number in the data. Sometimes it doesn't.</li>
</ul>
</li>
<li><strong><span style="color:#27ae60;">Step 2</span></strong>: Find the median of the first half.
<ul>
<li>This is the $Q_1$ value.</li>
</ul>
</li>
<li><strong><span style="color:#27ae60;">Step 3</span></strong>: Find the median of the second half.
<ul>
<li>This is the $Q_3$ value.</li>
</ul>
</li>
</ul>
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