Sample Variance

It’s also called the Unbiased estimate of population variance.

Refer to Khan academy: Sample variance

For a large population, it’s impossible to get all data. So we want to take out a number samples and calculate its variance.

The formula for Sample Variance is a bit twist to the population variance: let the dividing number subtract by 1, so that the variance will be slightly bigger.

It seems like some voodoo, but it’s reasonable. If we use the population variance formula for sample data, it's always gonna be underestimated.
That's why for sample variance we should do a bit change to the previous one.

Why we divide by n-1 for the Unbiased Sample Variance

Refer to Khan academy: Review and intuition why we divide by n-1 for the unbiased sample variance
Refer to Khan academy: Why we divide by n-1 in variance
Refer to Khan academy: Simulation showing bias in sample variance
Refer to Khan academy simulation: Unbiased Estimate of Population Variance

Simulation for different variance formulas with true variance:

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