Question

Find the interquartile range of the given dataset.

11, 13, 22, 17, 14, 21, 27, 15

(1 point)
Responses

13.5
13.5

6.5
6.5

8
8

21.5

Answer 1

To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).

To find Q1, we need to find the median of the lower half of the dataset.

Arranging the dataset in ascending order:
11, 13, 14, 15, 17, 21, 22, 27

The lower half of the dataset is:
11, 13, 14, 15

The median of the lower half is the average of the two middle numbers:
(Q1) = (13 + 14) / 2 = 13.5

To find Q3, we need to find the median of the upper half of the dataset.

The upper half of the dataset is:
17, 21, 22, 27

The median of the upper half is the average of the two middle numbers:
(Q3) = (21 + 22) / 2 = 21.5

The interquartile range is the difference between Q3 and Q1:
Interquartile range = Q3 - Q1 = 21.5 - 13.5 = 8

Therefore, the interquartile range of the given dataset is 8.