From AMS Glossary
A measure of variability (or spread).
It is denoted by σ2 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:
where E denotes expected value. The positive square root σ of the variance is called the standard deviation. An unbiased estimate s2 of the variance σ2 is obtained from n independent observations x1, x2, · · ·, xn and their sample average
and the positive square root s of s2 is taken as an estimate of the standard deviation σ.