Sample Variance

[umerkhan]

Hi all ... I want to know why we need sample variance when we already have our 'regular' formula for calculating variance. The following extract is from Miller, Chapter 3 ... Basic Statistics

 

[David Harper CFA FRM]

@umerkhan if by "regular" formula for variance, you are referring to σ^2(Y) = E(Y^2) - [E(Y)]^2, then the two versions are compatible but the E(Y) versions refers to the population variance. The sample variance will estimate the population variance, but it does not know the distribution. Consider a six-sided die: we know the distribution (uniform discrete) such that its variance can be retrieved with σ^2(Y) = E(Y^2) - [E(Y)]^2 = 15.167 - (3.5)^2 = 2.92. But realistically we often do not know the true (population) variance, so we might just have a sample of "die outcomes," e.g., {1, 5, 2, 6, 4, ....}. In which case, we need to use the sample variance above because we only have a set of observations. This sample variance returns an estimate (based on the estimator) of the unknown population variance. Notice the difference between observations, Y(1), Y(2) .... , and E(Y) or E(Y^2) which imply that we have distributional knowledge. I hope that helps!

 

[umerkhan]

Thank you Mr David