Question

Why is the descriptive standard deviation of a sample a biased estimate of population standard deviation? How do we correct for this bias?

Answer 1

A standard deviation refers to the descriptive statistical measure to know how deviated your dataset is from the mean. Sample variance is considered as the unbiased estimator while sample standard deviation does not and it is because that the sample standard deviation is the square root of sample variance. Square is considered as the concave function while bias is a downward function. Therefore, sample standard deviation is considered as the biased estimator of population standard deviation.

To make the standard deviation unbiased one needs to use Bessel's correction and according to which in the formula of sample standard deviation and variance, one needs to use the n - 1 instead of n.