# What is the expected value and the mean of sample standard deviation? [duplicate]

What is the expected value and the mean of sample standard deviation? I know that I can derive the expectation and variance of sample variance using the $\chi^2$ pdf. But I don't know how to start with sample standard deviation.

• The chi square only applies if you assume normality but you difn't state anything about distributions in your question. In the case of normality this question has been asked many times already. – Glen_b Jan 31 '17 at 17:42

## 1 Answer

If the sample is IID normal then the answer is

$$\sqrt{ \frac{2 \sigma^2}{n-1} } \times \frac{ \Gamma(n/2) }{ \Gamma( \frac{n-1}{2} ) }$$

where $\sigma^2$ is the population variance and $n$ is the sample size. For a full derivation read this.

Also, mean and expected value are the same thing.

• Thank you very much for the response. I actually want to derive this . So can anyone else hinted me a starting point ? – Sam88 Jan 28 '17 at 15:49
• Look at the link. It provides a full derivation, like I said in my answer. – gammer Jan 28 '17 at 16:23
• @dhanushkaSampath, yw – gammer Jan 29 '17 at 1:20