Measures of spread

Which measure of spread should I report?

The measure of spread to use will depend on which average value you have chosen to report for your dataset. As a general guide:

  • If you have reported the mode then you could report the range of the data.
  • If you have reported the median then you could report the interquartile range of the data.
  • If you have reported the mean then you could report the standard deviation of the data.

Range

The range of a data set is the difference between the smallest and largest values in the data set. 

To calculate the range, subtract the smallest number from the largest number (Range = Maximum - Minimum).

Example of range by Maths is Fun.

The range can be calculated in Excel by taking the difference between the maximum value and the minimum value of the dataset.

Interquartile range

The interquartile range (IQR) captures the middle 50% of ordered data. 

To calculate, order data from smallest to largest. Find the values that are at the first (Q1) and third (Q3) quartile (or 25% and 75% along). The interquartile range is the difference between the third and first quartile (IQR = Q3 - Q1).

Note: the second quartile is the median (Q2).

Example of interquartile range by Maths is Fun.

The interquartile range can be calculated in Excel by taking the difference between the third (=QUARTILE.EXC(datarange,3)) and first (=QUARTILE.EXC(datarange,1)) quartiles

Standard deviation

The standard deviation captures on average, how much each data point varies from the mean of the data set. 

Example of standard deviation by Maths is Fun.

How to calculate the population standard deviation using Excel.

How to calculate the sample standard deviation using Excel.


Additional resources

  • A short guide from the Statstutor with examples of how to perform the measures of spread calculations by hand and SPSS.
  • Practical examples and illustrations of measures of spread by Laerd statistics.