Range

The range of a set of numbers is from the minimum value to the maximum.  Whilst this provides the extent of the data, it may not be a "robust" measure as the extreme values may be "rogues" or "outliers" and not representative of the object of study.

Interquartile Range

Additional information can be derived from the Interquartile range which extends from the first to the third quartiles in which 50% of the values exist:

Box and Whisker Plot

The maximum and minimum values can be combined with the interquartile range in a graphic device known as a box and whisker plot:

Example

The example is based on observed windspeed at 1200 somewhere in the south of England:

The interquartile range indicates the "typical" condition where the windspeed will be betwenn 7.3 and 11.0 for 50% of the time.  In this case, the maximum value is important because it is very much bigger than the typical values, but it can be regarded as an extreme.

The box and whisker plot for the data is shown below:

Page updated: 29-Mar-2006

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