Question

What is the interquartile range of the data set: 9, 30, 2, 48, 42, 18, 81, 5, 55, 73, 11?

Answer 1

Interquartile range is `46`

Explanation:

Interquartile range measures variability, based on difference between third quartile and first quartile. It is defined as `Q_3-Q_1`.

To find first and third quartile, we should first arrange the data `{9,30,2,48,42,18,81,5,55,73,11}` in increasing order which is as follows.

`{2,5,9,11,18,30,42,48,55,73,81}`

As there are `11` data points, `Q_1` is `(11+1)/4` or `3^(rd)` data point i.e. `9`.

and `(11+1)xx3/4=9^(th)` data point i.e. `55`

Hence Interquartile range is `55-9=46`