Median

A measure of centre that marks the middle of a distribution of a numerical variable.

It is recommended that, for small data sets, this measure of centre is calculated by sorting the values into order and then counting the values, and to use software for large data sets.

The median is a stable measure of centre in that it is not influenced by unusually large or unusually small values. It is recommended that a graph of the distribution is used to emphasise its meaning as a feature of the distribution.

Example 1 (Odd number of values)

The maximum temperatures, in degrees Celsius (°C), in Rolleston for the first 9 days in November 2008 were: 18.6, 19.9, 20.6, 19.4, 17.8, 18.1, 17.8, 18.7, 19.6

Ordered values: 17.8, 17.8, 18.1, 18.6, 18.7, 19.4, 19.6, 19.9, 20.6

The data and the median are displayed on the dot plot below.

The median maximum temperature over these 9 days is 18.7°C. There are 4 values below 18.7°C and 4 values above it.

Example 2 (Even number of values)

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 mean of the two central values, 18.7 and 18.8, is 18.75.

The data and the median are displayed on the dot plot below.

The median maximum temperature over these 10 days is 18.75°C. There are 5 values below 18.75°C and 5 values above it.

Note: The median can be calculated directly from the dot plot or from the ordered values.

See: measure of centre

Curriculum achievement objectives references

Statistical investigation: Levels (5), (6), (7), (8)