Re: Why, for Sample Standard Deviation, Divide by N-1, Instead of N?


Kevin E. Thorpe wrote:
DarkProtoman wrote:
Why, when you calculate the sample standard deviation, you divide by
n-1, instead of n? I've heard someone said it has "nice mathematical
properties that make the math work out smoothly". What are those "nice
mathematical properties"? Thanks!!!!!

Supposing you have a random sample of observations from a population.
The sample variance \sum[(x_i - \bar{x})^2]/(n-1) is the unbiased
estimate
of the population variance. The standard deviation is the square root
of
this. It is actually the variance that has the "nice" properties
(unbiasedness,
its relation to the chi-squared distribution).

--
Kevin E. Thorpe
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto

OK, then, what are the nice mathematical properties of the variance,
then?

.

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