Range and Spread

The mean, median and mode all answer "where is the centre?". But two data sets can share the same centre and still look completely different — one tightly clustered, the other flung wide apart. Spread measures how stretched-out the data is. It is the other half of the story.

The range: crude but quick

The simplest measure of spread is the range: the gap between the largest and smallest values.

\text{range} = \max - \min.

It is instant to compute, but it is the crudest measure there is, because it depends on only two values — the two most extreme ones. A single outlier can blow the range up while the rest of the data hasn't moved at all. That fragility is why statisticians soon reach for sturdier measures of spread.

Watch one outlier stretch the range

Drag the orange point — the largest value — outward. The bracket spans from the minimum to the maximum, and the range grows with it, even though every other point stays put. One stray value, and the range balloons.