Physics307L F09:Schedule/Week 4 agenda/Calculating mean/Standard error

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:

[math]\displaystyle{ S_E = \frac{\widehat\sigma}{\sqrt{n}} }[/math]

where

[math]\displaystyle{ \widehat\sigma }[/math] 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

• [math]\displaystyle{ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}} }[/math]