Question

Walter selected 10 books at random from the children’s section of the library and recorded the number of pages in each. Paula selected 10 books at random from the adult fiction section of the library and recorded the number of pages in each.

Walter: 22, 40, 18, 25, 24, 30, 22, 32, 35, 20
Paula: 345, 355, 317, 441, 368, 510, 304, 418, 400, 362
Which statement correctly compares the interquartile ranges of the two data sets?

A.
The IQR for Paula’s data is 63 more than the IQR for Walter’s data.

B.
The IQR for Paula’s data is 87 more than the IQR for Walter’s data.

C.
The IQR for Paula’s data is 184 more than the IQR for Walter’s data.

D.
The IQR for Paula’s data is 355 more than the IQR for Walter’s data.

Answer 1

Sort and find quartiles.

Walter (sorted): 18, 20, 22, 22, 24, 25, 30, 32, 35, 40
Q1 = 22, Q3 = 32 ⇒ IQR = 32 − 22 = 10

Paula (sorted): 304, 317, 345, 355, 362, 368, 400, 418, 441, 510
Q1 = 345, Q3 = 418 ⇒ IQR = 418 − 345 = 73

Difference = 73 − 10 = 63, so answer A.