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For introductory statistics, should n be used as the divisor for the sample variance?

Terry Speed explores the age-old question every statistician is asked to answer at some point in their career….

“Why is the denominator in the sample mean n, but the denominator for the sample variance is n−1?”

Do you start talking about sample vs population, parameters vs statistics, bias, or a personal favorite.. “because you already spent one degree of freedom estimating the mean.”  Either way, it’s never a short, routine answer and the explanation might depend on the audience asking the question.  Then again, maybe in this day and age, just get a big enough sample and it doesn’t really matter.


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