What is Dispersion?

For $n$ results $x_1, \dots, x_n$ of mean $\bar x$, the experimental standard deviation is $s = \sqrt{\sum (x_i - \bar x)^2/(n-1)}$; it estimates $\sigma$. The standard deviation of the mean is the standard deviation of $\bar x$ over many series of $n$ results, estimated by $s/\sqrt n$.