Question

What is the interquartile range (IQR) of the following data set 17 16 21 15 25 22 18 23 17

Answer 1

IQR = 6

First locate the median $Q_{2}$ at the centre of the data arranged in ascending order. Then locate the lower and upper quartiles $Q_{1}$ and $Q_{3}$ located at the centre of the data to the left and right of the median.

Note that if any of the above are not whole values then they are the average of the values either side of the centre.

rearrange data in ascending order

15 16 ↓17 17 18 21 22 ↓23 25

                     ↑

$Q_{2}$ = 18

$Q_{1}$ = $\frac{16+17}{2}$ = 16.5

$Q_{3}$ = $\frac{22+23}{2}$ = 22.5

IQR = $Q_{3}$ - $Q_{1}$ = 22.5 - 16.5 = 6