The standard error of the mean (first used by Yule, 1897) is the theoretical standard deviation of all sample means of size n drawn from a population and depends on both the population variance (sigma) and the sample size (n) as indicated below:

sx-bar = (s2/n)1/2

where

s2 |
is the population variance and |

n |
is the sample size |

Since the population variance is typically unknown, the best estimate for the standard error of the mean is then calculated as:

sx-bar = (s2/n)1/2

where

s2 |
is the sample variance (our best estimate of the population variance) and |

n |
is the sample size |

See also, Descriptive Statistics Overview.