Centre and Spread

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

The median

Put the values in order and take the middle one. Half are below it and half above.

The range

The largest minus the smallest. It measures how spread out the values are.

When they disagree

One very large value drags the mean up but leaves the median almost alone.

Two numbers describe a data set

A measure of centre says where the values cluster. A measure of spread says how scattered they are. Reporting only the centre hides the difference between a consistent set and a wildly variable one with the same average.

The mean

Add all the values and divide by how many there are. The mean is the value everything would take if the total were shared equally, which is why it is sometimes called the fair-share value. It uses every data point.

The median

Sort the values and take the middle one. With an even count, average the middle two. The median depends only on position, so an extreme value can move it very little — which is exactly why it exists alongside the mean.

The range and its limits

The range is the largest value minus the smallest. It is easy to compute and easy to distort — one unusual value changes it completely while telling you nothing about the rest. It is a starting point for describing spread, not the end.