This blog post will focus on the **intuition** behind the divisor of the standard variance. No proofs, but lots of context and motivation.

And you’ll be pleased to know that this post is self contained. You don’t need to read either of my previous two posts on sample variance.

For a population the population variance is defined by

where

and for a sample the sample variance is defined by

where

And the question is “why doesn’t the sample variance have the same formula as the population variance?” i.e why isn’t the sample variance given by the **direct analogue** of the population variance, which is known as the “uncorrected sample variance”:

For the purpose of building intuition, there’s two facts that I think are extremely important to keep in mind.

Continue reading “Sample Variance Intuition”