Median

Description

The median is the middle value when a list of numbers is written in order. If there are two middle values, you find the mean of them.

Example: Find the median of 3, 9, 1, 7, 4.

First, order the values: 1, 3, 4, 7, 9

The median is 4.

Even number of values: Find the median of 2, 5, 8, 11.

The two middle values are 5 and 8, so the median is $\frac{5+8}{2} = 6.5$.

When is the median better than the mean?

The median is unaffected by outliers — extreme values that are much higher or lower than the rest. The mean gets pulled towards them, which can give a misleading picture.

Example: Seven people's weekly wages are £280, £290, £300, £310, £295, £285, £4200.

• Mean: $\frac{280+290+300+310+295+285+4200}{7} = \approx £851$ — distorted by the one high earner
• Median: £295 — a much more typical figure

In situations like house prices, salaries, or any data set with a few very large or very small values, the median is the fairer average to use.

Links

Ordering numbers Interquartile range Boxplots