Sampling Distribution of the Standard Deviation



The standard error of the standard deviation is approximately .

The approximation is more accurate for larger sample sizes (N > 16) and when the population is normally distributed. Try this simulation to explore the accuracy of the approximation.

The distribution of the standard deviation is positively skewed for small N but is approximately normal if N is 25 or greater. Thus, procedures for calculating the area under the normal curve work for the sampling distribution of the standard deviation as long as N is at least 25 and the distribution is approximately normal.