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

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the interquartile range of a dataset, we need to find the values of the first quartile (Q1) and the third quartile (Q3) and then subtract Q1 from Q3.

Step 1: Arrange the data in ascending order:
11, 13, 14, 15, 17, 21, 22, 27

Step 2: Find the median of the lower half of the data (Q1).
11, 13, 14, 15 (Q1 = 14)

Step 3: Find the median of the upper half of the data (Q3).
17, 21, 22, 27 (Q3 = 21.5)

Step 4: Calculate the interquartile range (IQR) by subtracting Q1 from Q3.
IQR = Q3 - Q1 = 21.5 - 14 = 7.5

Therefore, the interquartile range of the given dataset is 7.5.