Hey all,(adsbygoogle = window.adsbygoogle || []).push({});

In Schaum's outline it claims that the sample variance of s^2 is a biased estimate of the population variance because its mean is given by:

[tex] \mu_{s^{2}} = \frac{N-1}{N}\sigma^{2} [/tex]

which I am cool with. It then says that the modified variance given by:

[tex] \hat{s} = \frac{N}{N-1}s^{2} [/tex]

is an unbiased estimator. I know this should be really easy, but I don't know how to show it.

Also even if I accept that [tex] \hat{s}^{2} [/tex] is an unbiased estimator of the variance, Schaum's outline claims that [tex] \hat{s}[/tex] is a biased estimator of the population standard deviation. I don't see how this could be possible. if the variance is unbiased, and we take the square root of that unbiased estimator, won't the result also be unbiased ?

Thanks,

Thrillhouse

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Unbiased estimator of variance

**Physics Forums | Science Articles, Homework Help, Discussion**