Which data set has the greatest spread for the middle 50% of its data?

a) {18, 13, 22, 17, 21, 24}

b) {17, 19, 22, 26, 17, 14}

c) {13, 17, 12, 21, 18, 20}

d) {18, 21, 16, 22, 24, 15}

Option C.

Step-by-step explanation:

The highest Interquartile range represents the greatest spread for the middle 50% of its data.

Find the IQR of each data set.

Option A,

18, 13, 22, 17, 21, 24

Arrange the data in ascending order.

13, 17, 18, 21, 22, 24

Divide the data in 4 equal parts.

(13), 17, (18), (21), 22, (24)

Formula for IQR :

The IQR of first data set is

The IQR of the first data set is 5.

Similarly,

Option B,

17, 19, 22, 26, 17, 14

Arrange and divide the data in 4 equal parts.

(14), 17, (17), (19), 22, (26)

The IQR of the second data set is 5.

Option C,

13, 17, 12, 21, 18, 20

Arrange and divide the data in 4 equal parts.

(12), 13, (17), (18), 20, (21)

The IQR of the third data set is 7.

Option D,

18, 21, 16, 22, 24, 15

Arrange and divide the data in 4 equal parts.

(15), 16, (18), (21), 22, (24)

The IQR of the third data set is 6.

The IQR of third data set is highest, therefore third data set has the greatest spread for the middle 50% of its data.

Therefore, the correct option is C.