Definition:Variance/Discrete/Definition 1

Definition

Let $X$ be a discrete random variable.

Then the variance of $X$, written $\var X$, is a measure of how much the values of $X$ varies from the expectation $\expect X$, and is defined as:

$\var X := \expect {\paren {X - \expect X}^2}$

That is: it is the expectation of the squares of the deviations from the expectation.

Also see

• Equivalence of Definitions of Variance of Discrete Random Variable

Sources

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 2.4$: Expectation: $(21)$