Standard errors of the mean

The series of sample means x¯₁, x¯₂, x¯₃ ........ is normally distributed or nearly so as according to the central limit theorem. This can be described by its mean and its standard deviation. Its standard deviation is termed as the standard error.

Standard error of the mean is =  S_x¯ = s/√n

Note: the above formula is satisfactory for larger samples and a large population that is n > 30 and n > 5 percent of N.

- The word 'error' is in place of 'deviation' to emphasize that variation with sample means is because of sampling errors.

- The smaller the standard error the greater the precision of the sample value.