The standard error (SE) of a statistic is the variance of its sample distribution or an estimate of that standard deviation. If the statistic is the sample mean, then the SE is called the standard error of the mean (SEM). The standard error is a key ingredient in producing confidence intervals. 1

Standard Error of the Sample Mean

For a population with a population standard deviation , if we take independent samples of observations, the standard error of the sample mean is given by:

In practice, the population standard deviation is often unknown. In such cases, the sample standard deviation is used as an estimate, resulting in the following formula:

Footnotes

  1. Standard error - Wikipedia