Question

What is the interquartile range of this set of data?

Answer 1

Answer: The interquartile range of this set of data is 19.

Explanation:

The values in the given data set : 15, 19, 20, 25, 31, 38, 41

Total values : n= 7

First arrange them in ascending order, we get

15, 19, 20, 25, 31, 38, 41

Lower quartile =
`(1)/(4)(n+1)^{\text{th}}\text{value}`

`=(1)/(4)(7+1)^{\text{th}}\text{value}\\\\=2^{\text{nd}}\text{value}\\\\=19`

Upper quartile =
`(3)/(4)(n+1)^{\text{th}}\text{value}`

`=(3)/(4)(7+1)^{\text{th}}\text{value}\\=3(2)^{\text{th}}\text{value}\\=6^{\text{th}}\text{value}\\=38`

Interquartile range = Upper quartile -Lower quartile

= 38-19=19

Hence, the interquartile range of this set of data is 19.