Standard deviation

Math

Definition

A measure of how spread out data values are from the mean. A small standard deviation means data points are clustered near the mean, while a large one means they are more spread out. It is calculated as the square root of the variance.

Examples

  • Test scores {90, 92, 88, 91, 89} have a small standard deviation because they're close together
  • Test scores {50, 70, 90, 100, 40} have a large standard deviation because they're widely spread
Key Fact

s = √[Σ(xᵢ − x̄)² / (n − 1)] for sample standard deviation

Related Terms

Mean median mode Normal distribution Random variables Sampling distribution of a mean

Study This Concept

Practice standard deviation with free review games in these units:

AP Statistics Unit 1: Exploring One-Variable Data