Editing Standard error (section)

=== Exact value ===
Suppose a statistically independent sample of <math>n</math> observations <math> x_1, x_2 , \ldots, x_n </math> is taken from a [[statistical population]] with a [[standard deviation]] of <math>\sigma</math> (the standard deviation of the population). The mean value calculated from the sample, <math>\bar{x}</math>, will have an associated ''standard error on the mean'', <math>{\sigma}_\bar{x}</math>, given by:<ref name=":0" />

<math display="block">{\sigma}_\bar{x} = \frac{\sigma}{\sqrt{n}}.</math>

Practically this tells us that when trying to estimate the value of a population mean, due to the factor <math>1/\sqrt{n}</math>, reducing the error on the estimate by a factor of two requires acquiring four times as many observations in the sample; reducing it by a factor of ten requires a hundred times as many observations.