Variance of Sample Mean

Theorem
Let $X_1, X_2, \ldots, X_n$ form a random sample from a population with mean $\mu$ and variance $\sigma^2$.

Let:


 * $\ds \overline X = \frac 1 n \sum_{i \mathop = 1}^n X_i$

Then:


 * $\var {\overline X} = \dfrac {\sigma^2} n$