# 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.

## marked as duplicate by Glen_bJan 31 '17 at 17:48

• 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

$$\sqrt{ \frac{2 \sigma^2}{n-1} } \times \frac{ \Gamma(n/2) }{ \Gamma( \frac{n-1}{2} ) }$$
where $\sigma^2$ is the population variance and $n$ is the sample size. For a full derivation read this.