Variance and Standard Deviation

While expected value tells us the average outcome, variance and standard deviation tell us how much the outcomes tend to differ from the mean.

Variance is defined as the expected squared deviation from the mean, and gives a sense of spread or risk in squared units.

\[\text{Var}(X) = E[(X - \mu)^2].\]

Standard deviation or \( \sigma \) is the square root of variance and is often preferred because it's in the same units as the original data.

\[\sigma = \sqrt{\text{Var}(X)}.\]