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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.

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It is the standard deviation of sample mean.

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 $\textit{s.e.}(\bar{x}) = \sqrt{var(\bar{x})} = \sqrt{\sigma^2/N}$.

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  • $\begingroup$ \frac{\sigma}{\sqrt{n}} is also another equivalent it if anyone forgot their square root rules. Remember this is not the standard deviation which had me confused. $\endgroup$
    – samman
    Jun 30 '16 at 1:56
  • $\begingroup$ Forgot to check it. I can't get the math to show correctly whats up with that. Was trying to fix it before I answered corrected. It worked in question text box when I add comment it doesn't format it. Is it showing correctly in your browser. $\endgroup$
    – samman
    Jun 30 '16 at 2:02
  • $\begingroup$ Would you say this is also known as standard error of the mean. I want to fix my subject of the question so it won't be generic. I didn't know what to call my subject till after I got my answer. $\endgroup$
    – samman
    Jun 30 '16 at 2:20

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