interquartile range

To find the interquartile range, we must first sort the data into ascending order. Let’s use the sets of data below as an example:

Even set of data	3, 4, 2, 8, 12, 6
	2, 3, 4, 6, 8, 12

Odd set of data	4, 4, 3, 4, 7, 8, 10
	3, 4, 4, 4, 7, 8, 10

We can then proceed to find the median.

In the even set of data, the median (mid-point) is between 4 and 6:

2, 3, 4,| 6, 8, 12

In the odd set of data, the median (mid-point) is 4:

3, 4, 4,4 7, 8, 10

We can now find the mid-points either side of the median.
In the even set of data, the mid-points are between 3 and 8:

2,3, 4,| 6,8, 12

The lower quartile = 3
The upper quartile = 8

In the odd set of data, the mid-points are between 4 and 8:

3,4, 4,4 7,8,10

The lower quartile = 4
The upper quartile = 8

In order to find the interquartile range, we must subtract the lower quartile number from the upper quartile number:

Even data: 8 – 3 = 5
Odd data: 8 – 4 = 4