# The sample variance as a biased estimator of the population variance

There is the theory that the use of the entire number of sample observations, n, instead of n - 1 as the divisor in the computation of the sample variance, will systemically underestimate the population parameter. That underestimation causes the sample variance to be a biased estimator of the population variance.

Why is using n - 1 instead of n as an deminator improving the statistical properties of the sample varinace as an estimator of the population variance. Is there a mathematical (calculus) explanation or is there any intuition behind it?

Just find the Schweser description for that not very helpful to understand it.

Can someone deliver a better explanation.

Thanks

PW

Excellent explanation:

P.S.: Khan Academy is also nice for some other topics in Level I, e.g. Economics and Derivatives.

Best,

Oscar

This might be worth a look as well. http://www.ee.columbia.edu/~dliang/files/mle_biased.pdf

I wrote a brief article on the sample standard deviation that touches (lightly) on this: http://financialexamhelp123.com/sample-standard-deviation/