[doormat]

I don't know a better formula but I found this reference which may or may not be helpful:

Sample standard deviation: The sample variance is an unbiased estimator of the parametric variance. Taking the square root of the sample variance does not give an unbiased estimator of the parametric standard deviation. A rather complicated exact correction factor, and a simpler approximate correction factor, are given on p. 53 of Sokal and Rohlf.

doormat