The nerdiest question ever

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1

<p>My friends and I were fighting about the following. What is the "middle 50 percent" when you have less than 25 percent of the kids with a top score. </p>

<p>Here's the example, made simple. Score breakdown for 100 admits</p>

<p>36: 6 kids</p>

<p>35: 44 kids</p>

<p>34: 25 kids</p>

<p>33: 10 kids</p>

<p>32: 10 kids</p>

<p>31: 5 kids</p>

<p>Now would you say the "middle 50 percent" was 34-35? A quarter of kids ARE under that. But less than a quarter are abvoe it. Would it be something else? Any thoughts.</p>

2

<p>Literally, write out those numbers as if you were finding the average of them. The first twenty five would make up the bottom 25% so on and so forth. </p>

<p>I’m unsure of how colleges define their middle 50% so interpret it as you wish.</p>

3

<p>34-35 would be correct.</p>

<p>Say we have 16 kids (an easy number divisible into quarters) and their scores are…
31 - 1 kids
32 - 3 kids
33 - 4 kids
34 - 3 kids
35 - 3 kids
36 - 2 kids</p>

<p>Lay it out like this…</p>

<p>31, 32, 32, 32, 33, 33, 33, 33, 34, 34, 34, 35, 35, 35, 36, 36</p>

<p>Go in 4 from each end (4 is 25% of 16) and make cuts.</p>

<p>31, 32, 32, 32, | 33, 33, 33, 33, 34, 34, 34, 35, | 35, 35, 36, 36</p>

<p>In this case, the mid-50% range would be 33 to 35. Even though there are a few other 35s beyond the mid-range, the top 75% mark ends within that group of 35s, hence 35 is the top of the mid-range. Make sense?</p>

4

<p>IQR=Q3-Q1</p>

<p>So for Q3 find the top half and find the median of that.
For Q1 find the bottom half and find median of that.</p>

5

<p>Seriwe. Yes, it does. Our fight was over whether if you have a 33-35 “middle 50 percent” that means that, for certain, 25 percent have a 36. I said no.</p>

6

<p>The 1st and 3rd quartiles are defined as the median of the bottom and top halves of data (not including the median). So remove the median, then find the quartiles. The IQR is simply the positive difference between them.</p>