Definition: The Sampling Distribution of Standard Deviation estimates the standard deviation of the samples that approximates closely to the population standard deviation, in case the population standard deviation is not easily known. Thus, the sample standard deviation (S) can be used in the place of population standard deviation (σ). Symbolically,
The standard deviation of the distribution of the sample standard deviation drawn from the normal population is called as the standard error of the standard deviation and is denoted by S, which can be computed by using the following formula:
The sampling distribution of standard deviation is likely to be normal when the sample size ‘n’ is large and whereas it is positively skewed if the sample size ‘n’ is small. The sample is said to be large when n ≥ 25.