# Variance

From AMS Glossary

## variance

A measure of variability (or spread).

It is denoted by σ where and the positive square root

^{2}and defined as the mean-square deviation from the mean, that is, the mean of the squares of the differences between individual values of*x*and the mean value μ:*E*denotes expected value. The positive square root σ of the variance is called the standard deviation. An unbiased estimate*s*^{2}of the variance σ^{2}is obtained from*n*independent observations*x*_{1},*x*_{2}, · · ·,*x*_{n}and their sample average as follows:*s*of*s*^{2}is taken as an estimate of the standard deviation σ.