Estimated standard error

In most applications, the population standard deviation, σ, is unknown, but the standard error can still be evaluated if it is replaced by the sample standard deviation, s.

Warning
Standard statistical notation is a little confusing here. The term "standard error" is used for both the theoretical standard deviation of the errors and for our best estimate of it.

Examples

The following data sets were collected to provide information about underlying populations whose characteristics were unknown. In each case, the sample mean provides an estimate of the population mean and the standard error gives information about the accuracy of this estimate.