What is the interquartile range of this set of data?
15, 19, 20, 25, 31, 38, 41

Explanation:

If the data wasn't sorted, then the first step would be to arrange the elements from smallest to largest. However, that is already done for us.

The middle most value in the set {15, 19, 20, 25, 31, 38, 41} is 25 because there are three values below it {15,19,20} and three values above it {31,38,41}

Focus on the lower half {15,19,20} and note the middle of this subset is element 19. This is the value of Q1 or the first quartile.

The third quartile Q3 is 38 because the middle of the upper half data set {31,38,41} is 38.

We now subtract the values of Q3 = 38 and Q1 = 19 to get the interquartile range (IQR)

IQR = Q3 - Q1 = 38 - 19 = 19

answer: 2/4

step-by-step explanation: