Variance and Standard Deviation of a Random Variable | Why We Square the Deviations

Two random variables with the same expected value 3.5: one takes 3 and 4, the other 1 and 6. Which one is more spread out, and how do we measure it? The deviations average out to 0, so we square the deviations, and the squares are drawn as real squares on the chart. Then the variance, the standard deviation σ as the typical distance from the mean, a die (Var = 35/12, σ ≈ 1.71), the shortcut Var(X) = E(X²) − (E(X))² with its proof, and three properties: Var(X + 2) = Var(X), Var(2X) = 4 Var(X), and the variances of two independent dice add up while σ does not. Animated on the board: no voice, just the mathematics. 0:00 Two variables, one expected value 0:14 Deviation from the mean 0:46 Variance 1:32 Standard deviation 2:11 A die 2:40 A shortcut formula 3:39 Properties 4:35 Summary #probability #variance #standarddeviation #math #tutor