Question

Find the interquartile range of the given dataset.

11, 13, 22, 17, 14, 21, 27, 15

(1 point)
Responses

21.5
21.5

6.5
6.5

8
8

13.
pick one of these answers

Answer 1

To find the interquartile range (IQR) of the dataset, we first need to sort the dataset and then find the first quartile (Q1) and third quartile (Q3).

Given dataset:
11, 13, 22, 17, 14, 21, 27, 15

**Step 1: Sort the data**
Sorted data:
11, 13, 14, 15, 17, 21, 22, 27

**Step 2: Find Q1 and Q3**
- Q1 (the first quartile) is the median of the first half of the data.
First half: 11, 13, 14, 15
Median of the first half (Q1) = (13 + 14) / 2 = 13.5

- Q3 (the third quartile) is the median of the second half of the data.
Second half: 17, 21, 22, 27
Median of the second half (Q3) = (21 + 22) / 2 = 21.5

**Step 3: Calculate the interquartile range**
IQR = Q3 - Q1 = 21.5 - 13.5 = 8

Based on your options, the answer is:
**8**