|This article/section deals with mathematical concepts appropriate for late high school or early college.|
where the expected value of X is E(X).
Thus the standard deviation is
The formula for standard deviation must not be confused with the formula
(where is the sample mean).
which is the formula for a point estimate of the true standard deviation from a sample size of n. As such this statistical estimator itself has a variance which, as the formula indicates, decreases as the sample size increases.