# Interquartile Range

## What is the interquartile range?

The inter-quartile range shows the spread of a data set but is more accurate than using the range because it removes extremes. The inter-quartile range shows the spread of the middle 50 per cent of the data set because it removes the top and bottom 25%. It gives a better indication of how data is spread around the median value. The values are then divided into four equal groups or quartiles, where n is the number of values.

The upper quartile is the value that occurs in the following position:

__(n+1) __= Upper quartile (UQ)

4

The lower quartile is the value that occurs in the following position:

__3(n+1) __= Lower quartile (UQ)

4

The difference between the two values is known as the interquartile range. In the worked example below, we explore two approaches to calculating the interquartile range.

## Calculating the interquartile range

The rainfall data below has been ranked in order and has been presented on a graph.

*Approach 1*

To work out the interquartile range for the rainfall data:

Lower quartile = 11+1 = __12__ = 3

4

Third position = 180

Upper quartile = 3×12 = __36__ = 9

4

Nineth position = 342

Therefore, the interquartile range is the difference between 180 and 342 = 162mm

*Approach 2*

Another way to calculate the interquartile range is to rank the data from lowest to highest e.g.

## Statistical Techniques in Geography

Use the images below to explore related GeoTopics.