# Physics307L F07:Schedule/Week 4 agenda/Calculating mean/Standard error

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From wikipedia

See also: http://support.microsoft.com/kb/214076

## 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:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle S_E = \frac{\widehat\sigma}{\sqrt{n}}}**

where

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}}**