Question

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Question
Find the interquartile range of the given dataset.

11, 13, 22, 17, 14, 21, 27, 15

(1 point)
Responses

6.5
6.5

13.5
13.5

21.5
21.5

8
8
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Answer 1

To find the interquartile range (IQR) of the dataset, we first need to organize the data in ascending order and then determine 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 is the median of the first half of the data. The first half is: 11, 13, 14, 15
- The median of 11, 13, 14, and 15 (the average of the two middle numbers 13 and 14):
- Q1 = (13 + 14) / 2 = 13.5

- Q3 is the median of the second half of the data. The second half is: 17, 21, 22, 27
- The median of 17, 21, 22, and 27 (the average of the two middle numbers 21 and 22):
- Q3 = (21 + 22) / 2 = 21.5

**Step 3: Calculate the IQR**

IQR = Q3 - Q1 = 21.5 - 13.5 = 8

So, the interquartile range of the dataset is **8**.

**Answer**: 8