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A measure of spread for a distribution of a numerical variable which is the width of an interval that contains the middle 50% (approximately) of the values in the distribution. It is calculated as the difference between the upper quartile and lower quartile of a distribution.
It is recommended that, for small data sets, this measure of spread is calculated by sorting the values into order or displaying them on a suitable plot and then counting values to find the quartiles, and to use software for large data sets.
The interquartile range is a stable measure of spread in that it is not influenced by unusually large or unusually small values. The interquartile range is more useful as a measure of spread than the range because of this stability. It is recommended that a graph of the distribution is used to check the appropriateness of the interquartile range as a measure of spread and to emphasise its meaning as a feature of the distribution.
Example
The maximum temperatures, in degrees Celsius (°C), in Rolleston for the first 10 days in November 2008 were: 18.6, 19.9, 20.6, 19.4, 17.8, 18.1, 17.8, 18.7, 19.6, 18.8
Ordered values: 17.8, 17.8, 18.1, 18.6, 18.7, 18.8, 19.4, 19.6, 19.9, 20.6
The median is the mean of the two central values, 18.7 and 18.8. Median = 18.75°C
The values in the ‘lower half’ are 17.8, 17.8, 18.1, 18.6, 18.7. Their median is 18.1. The lower quartile is 18.1°C.
The values in the ‘upper half’ are 18.8, 19.4, 19.6, 19.9, 20.6. Their median is 19.6. The upper quartile is 19.6°C.
The interquartile range is 19.6°C – 18.1°C = 1.5°C
The data and the interquartile range are displayed on the dot plot below.
See: lower quartile, measure of spread, quartiles, upper quartile
Curriculum achievement objectives references
Statistical investigation: Levels (5), (6), (7), (8)
