Find the quartiles for these data values: 5, 7, 7, 8, 10, 11, 12, 15, 17.

A. Q1 = 7, Q2 = 11, Q3 = 15

B. Q1 = 7, Q2 = 10, Q3 = 13.5

C. Q1 = 6, Q2 = 9, Q3 = 12

D. Q1 = 7.5, Q2 = 10.5, Q3 = 13.5

The answer is B. Q1 = 7, Q2 = 10, Q3 = 13.5.

Solution:

Since the nine values are already arranged in ascending order, we can easily see that the median is 10. Hence Q2 = 10.

We can find the first quartile Q1 by getting the median in the lower half of the data

5, 7, 7, 8

that is, Q1 = (7 + 7) / 2 = 7

We can find the third quartile Q3 by getting the median for the upper half of the data

11, 12, 15, 17

that is, Q3 = (12 + 15) / 2 = 13.5