Mean, Median, and Which to Trust

The mean shares the total out equally: add everything, then divide by how many there are.

The median

Put the values in order and take the middle one. With an even count, take the halfway point of the middle two.

What an outlier does

For 2, 3, 4, 5 and 86, the mean is 20 — larger than four of the five values. The median is 4.

Which one to report

When one value is far from the rest, the median describes the set more honestly.

One outlier can move the mean a long way

Five people earning £20,000 and one earning £500,000 have a mean income of £100,000 — a figure nobody earns. The median is £20,000, which describes the group far better. The mean uses every value, so every value can drag it.

Which to use

Use the mean when the data are roughly symmetric with no extreme values. Use the median when the data are skewed or contain outliers. House prices and incomes are almost always reported as medians, for exactly this reason.

The mode

The mode is the most frequent value. It is the only measure that works for categories — you cannot average favourite colours. A data set can have two modes, or none, which limits how often it is useful.

Choosing a statistic is an honesty question

Someone wanting to make average pay look high will quote the mean; someone wanting it low will quote the median. Both are true statements. Knowing which measure suits the data is what lets you read a claim critically rather than just accepting the number.