Answer: IQR = 8
IQR is shorthand for interquartile range
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Step-by-step explanation:
The original list is {84,75,90,87,99,91,85,88,76,92,94}
It sorts to {75,76,84,85,87,88,90,91,92,94,99}
Pick out the middle most value, which is 88 in slot 6. A quick way to get here is to see that there are n = 11 values in this set. So n/2 = 11/2 = 5.5 which rounds to 6, and that tells us the slot number where the median is held. If n is an even number, then you'll need to use the midpoint formula for the two middle-most items.
After we determine the median is 88, we split the sorted data set as follows:
L = {75,76,84,85,87}
U = {90,91,92,94,99}
Everything in set L is below the median. L for lower.
Everything in set U is above the median. U for upper.
Sets L and U have 5 items each. Note that 5+1+5 = 11 = n.
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The median of set L is 84, so Q1 = 84
The median of set U is 92, so Q3 = 92
Q1 and Q3 are the first and third quartiles respectively. Subtracting them gets us the IQR (interquartile range)
IQR = Q3 - Q1
IQR = 92 - 84
IQR = 8
The IQR helps give us a sense how spread out the data set is. It's similar to the range, which is found by range = max - min. The larger the (interquartile)range, the more spread out the data set will be.