Median

The median is the middle value of a dataset once its values are sorted in order, splitting the data so that half the values fall below it and half above.

The median is a measure of the centre of a dataset, like the average (mean) — but it is found by position rather than by arithmetic. Sort the values from smallest to largest and the median is the one in the middle. Because it depends only on rank, a single very large or very small value cannot drag it far, which makes it a robust summary when the data is skewed.

How the median is found

With an odd number of values, the median is simply the middle one. With an even number there are two middle values, so the median is taken as their average. The key contrast is with the mean: the mean adds everything up and divides, so one extreme value pulls it strongly, whereas the median barely moves. When the mean and median differ a lot, the data is lopsided.

A concrete example

Take five values sorted in order: 3, 5, 8, 9, 40. The median is the middle one, 8, because two values lie below it and two above. The mean, by contrast, is 13 — pulled upward by the single large value of 40. This gap shows why the median is often the fairer "typical" figure: it reports what a middle member of the group actually looks like, undistorted by one extreme.

How the median appears in a chart

On a box plot, the median is the line drawn inside the box, marking the centre of the distribution. It is also the value at the 50th percentile, sitting exactly between the lower and upper halves of the data.

Related terms

The median is the second quartile, the middle of the three cut points that divide sorted data into four parts. Its resistance to extreme values is what distinguishes it from the mean when an outlier is present. See where the median is drawn in the histogram guide.