Variance
Also: Var(X), standard deviation, σ²
Var(X) = E[(X − μ)²] = E[X²] − (E[X])². Its square root, the standard deviation σ, is in the same units as X. Averaging n independent samples divides the variance by n.
Var(X) = E[(X − μ)²] = E[X²] − (E[X])²
Example
For a fair die, E[X²] = 91/6 ≈ 15.17 and E[X] = 3.5, so Var(X) = 15.17 − 12.25 ≈ 2.92 and σ ≈ 1.71.