This is NOT a proof of Bessel's correction. Instead, we explore several ideas to help you understand why the "n-1" makes sense. It boils down to the fact that we (usually) don't know the population mean when we are estimating the variance.
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1:52 Overview of the Pieces we will explore
6:10 Sample means minimize the formula
15:11 Simulations in Rstudio
20:11 Dividing by N makes estimates too small
26:50 If we know the population mean, we can divide by N!
28:40 Using Bessel Correction also gives unbiased estimates