# Standard deviation of sample mean - unknown equation answered

Does anyone recognize mathematically or statistically what this formula's purpose is. If it is not statistically useful what does dividing a value by a constant and taking a square root mean? For example taking a sum values divided by total number of values equates to average. If I can get the mathematical name of this operation. N in this case being the number of samples in a set.

$\sqrt{\sigma^2/N}$

This is relevant to another larger question I posted but felt that this may be useful by itself.

If you have $N$ i.i.d. samples $x_1, x_2, \cdots, x_N$, where $var(x_i) = \sigma^2$, and $\bar{x} = \frac{1}{N}\sum_{i=1}^{N}x_i$, then $var(\bar{x}) = \frac{\sigma^2}{N}$. Hence $\textit{s.e.}(\bar{x}) = \sqrt{var(\bar{x})} = \sqrt{\sigma^2/N}$.