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.