To understand how population variance differs from sample variance, let’s break down what happens during the transition from population formulas to sample estimators:

μ is replaced by x̄

When calculating sample variance, we do not know the population mean (μ), so we estimate it using the sample mean (x̄). This is a key shift from population to sample statistics.

N is replaced by n – 1

In sample variance, the denominator becomes (n – 1) instead of N (population size). This adjustment is called Bessel’s correction, and it’s used to reduce bias when estimating population variance from a sample.