Find the interquartile range of the data.

84,75,90,87,99,91,85,88,76,92,94

IQR is shorthand for interquartile range

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.

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.

c

step-by-step explanation: