# Physics307L:Schedule/Week 4 agenda/Calculating mean/Standard error

From wikipedia

## Standard error of the mean

The standard error of the mean of a sample from a population is the standard deviation of the sampling distribution of the mean, and may be estimated by the formula:

$S_E = \frac{\widehat\sigma}{\sqrt{n}}$

where

$\widehat\sigma$ is an estimate of the standard deviation σ of the population, and
n is the size (number of items) of the sample.

Note: Standard error may also be defined as the standard deviation of the residual error term. (Kenney and Keeping, p. 187; Zwillinger 1995, p. 626)

## Standard errors

### Single sample

• $\sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$