Standard Deviation of Sample Mean Calculator

What the Standard Deviation of the Sample Mean Measures

When you draw many samples of size $n$ from a population, the sample means form a sampling distribution. Its spread is the standard deviation of the sample mean, also called the standard error when population $\sigma$ is known:

$$\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}$$

Smaller values mean sample means cluster closer to $\mu$. Related tools: Central Limit Theorem Calculator and Standard Error Calculator.

Example

If $\sigma = 7.1$ and $n = 100$, then $\sigma_{\bar{X}} = 7.1 / \sqrt{100} = 0.71$. Sample means vary much less than individual observations.