It seems logical that this formula would also provide a good estimate of the variance of the population when only given a sample. This is what is called and 'estimator'. However, this cannot be used to estimate the population variance based on a sample from it, i.e. it is biased. A proof of this follows along with the alternative, unbiased estimator of the variance of the population.
Please excuse the poor quality.
I can understand if some of this proof is not clear, if you have any queries I can do my best to explain, please leave a comment.
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