1

Problem

Find the interquartile range(IQR) 8, 12, 13, 19, 22, 25, 7, 14, 5, and 16.

2

Step

Given the data sets

8, 12, 13, 19, 22, 25, 7, 14, 5, and 16

The ascending order of the given set is 5, 7, 8, 12, 13, 14, 16, 19, 22, and 25.

3

Step

First, we have to find the first quartile and third quartile ranges Q1 and Q3

→ Q1 is the median of the lower half of the data: (5, 7, 8, 12, and 13) = 8

→ Q3 is the median of the upper half of the data:(14, 16, 19, 22, and 25) = 19

4

Formula

Inter Quartile Range(IQR) = Q3 - Q1.

5

Step

Now, we can calculate the interquartile range (IQR) using the formula

→ IQR = Q3 − Q1

→ IQR = 19 - 8 = 11

6

Solution

Therefore, the quartile range(IQR) for the given dataset is 11.

7

Sumup

Please summarize steps

Choices

8

Choice-A

This option is correct because 11 is the accurate inter-quartile range for the given dataset

Correct 11

9

Choice-B

This option is incorrect. Although 13 is close to the actual IQR value, it is higher than the actual IQR value

Wrong 13

10

Choice-C

This option is incorrect because 9 is not accurate when compared to the actual value of IQR

Wrong 9

11

Choice-D

This option is incorrect because 17 is very much higher than the actual IQR value for a given dataset

Wrong 17

12

Answer

Option

A

13

Sumup

Please summarize choices