Mathematics · Glossary

What is Variance?

Definition 18.12 High School Mathematics · Chapter 18 — Probability and Random Variables

The variance of XX measures the spread of its values around the expectation m=E(X)m = \E(X):

V(X)=E((Xm)2)=i=1kP(X=xi)(xim)2,σ(X)=V(X).\V(X) = \E\bigl((X - m)^2\bigr) = \sum_{i=1}^{k} \P(X = x_i)\,(x_i - m)^2, \qquad \sigma(X) = \sqrt{\V(X)} .
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