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Question:

Why do we divide by (n-1) and not n?

Answer:

The sample variance is not actually the mean of the squared deviations, because we divide by (n-1) instead of n. In statistical inference (described in detail in another module) we make generalizations or estimates of population parameters based on sample statistics. If we were to compute the sample variance by taking the mean of the squared deviations and dividing by n we would consistently underestimate the true population variance. Dividing by (n-1) produces a better estimate of the population variance. The sample variance is nonetheless usually interpreted as the average squared deviation from the mean.