, {\displaystyle S^{2}} { MathWorldA Wolfram Web Resource. ~ The expression for the variance can be expanded as follows: In other words, the variance of X is equal to the mean of the square of X minus the square of the mean of X. , is the covariance, which is zero for independent random variables (if it exists). 1 When variance is calculated from observations, those observations are typically measured from a real world system. {\displaystyle \sigma _{X}^{2}} ) Variance analysis can be summarized as an analysis of the difference between planned and actual numbers. X 4 a c How to Calculate Variance. In general, for the sum of T ( ( x where are random variables. We take a sample with replacement of n values Y1,,Yn from the population, where n

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