Kathryn Kingham

Find the interquartile range of this set of data: 96, 52, 87, 114, 76, 101, 76, 114, 99, 96, 88, 111, 88, 94, 53.

Find the interquartile range of this set of data. The first thing we’re gonna do here to find our interquartile range is to order of values from least to greatest. Looking across the list, it looks like 52 is the smallest. After that, I notice a 53. I can’t see any values in the 60 range. I see 76. Actually, two values of 76. Next comes 87. 88 is represented twice. Next is 94. We have 96 repeated twice. Next is 99, followed by 101, and 111, and then we have 114 two times. Now I can move on to step two and find the median of our data, the value that’s in the middle

There are 15 total pieces of data in this set. And because 15 is an odd number, we’ll have a middle exactly. There would be seven values on either side of the median. 94 is the median. Now we’ll need to find the median of the first half and the median of the second half. Starting with the first half, I see that there are three values before the 76 and three values after 76. This makes 17 [76] the middle of the first half. We also could call it quartile one or Q1.

I’ll now do the same thing for the second half of the data. I wanna find the middle of the second half, so there are three values before 101 and there are three values after 101. This means 101 is the middle of the second half. It’s our third quartile or Q3. The interquartile range is the distance from the middle of the first half to the middle of the second half. The distance from Q1 one to Q3. Q3 minus Q1 equals the interquartile range. We substitute our Q3 and our Q1 and say 101 minus 76 equals 25. The interquartile range of this data set equals 25.

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