Standard error of the mean

The standard error of the mean measures the spread of the sampling distribution of $\bar{x}$ (x-bar, the sample mean), so it shrinks as the sample grows. In practice you compute $SE_{\bar{x}} = \frac{s}{\sqrt{n}}$ from the sample standard deviation s; if you somehow knew the population standard deviation $\sigma$ (sigma), you would use $\frac{\sigma}{\sqrt{n}}$ instead. For example, with s = 12 and n = 36 the standard error is $12/\sqrt{36} = 12/6 = 2$. Watch the square root: cutting the standard error in half takes four times as many observations.