How is the sample variance an unbiased estimator?

Q&A
#1

In the R Data Analyst “Measure Variability” lesson, we are told that

In the previous screen, we stated that statisticians agree that n-1 is better than n or n-2 for calculating the sample standard deviation. An argument supporting this comes from the fact that the sample variance s^2 which uses n-1 is an unbiased estimator for the population variance σ^2

So my questions are, what exactly is an unbiased estimator? How is just stating that “variance is an unbiased estimator” enough of an argument for the use of n-1? Why is the standard deviation of a sample not an unbiased estimator of of the population SD?

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#2

Hiii @39230239.jakaka,

An unbiased estimator means sample variance mostly similar to the true population variance. There are multiple experiments had been done to prove n-1 works better than n or n-2.

For better understanding, I suggest that you watch this two videos from Khan Academy which answers all of your questions.

Theory video which gives intuition behind this.

Simulation which shows practical implementation.

Hope it helps!!

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