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Find the interquartile range of the set of data: 29.7, 36.2, 29.1, 11.7, 45.3, 19.6, 42.8, 57.9, 51.9, 42.9, 51.2, 5.4, 29.2, 15.4, and 11.6.
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The first thing that we should do is put these numbers in ascending order, smallest to largest.
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Our smallest number is 5.4, then 11.6, then 11.7.
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Next is 15.4, then 19.6, then 29.1.
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Next is 29.2, now 29.7, 36.2, 42.8, 42.9, 45.3, 51.2, 51.9, and lastly 57.9.
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So now we need to find the median, the middle number.
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There are 15 total numbers.
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So what is the middle of 15?
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That would be eight.
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There are seven numbers on each side of that number.
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So that eighth number would be in the middle.
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So 29.7 is our median.
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Now our next step is to find the middle of this lower half and the middle of the upper half.
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Out of seven numbers, the fourth one would be the middle because there would be three numbers on each side, so 15.4.
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And then on the upper half, it would be 45.3.
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So we are finding the interquartile range.
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Now let’s think about this: quartile, four.
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Here’s one quarter of our numbers, another quarter or quartile, a third, and a fourth.
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So the interquartile range is the range between the interquartiles.
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So we need to take 45.3 and subtract 15.4, resulting in an interquartile range of 29.9.