Standard deviation of a random variable

The standard deviation of a random variable measures typical distance from the mean, weighting every squared deviation by its probability: $\sigma_X = \sqrt{\sum (x_i - \mu_X)^2 P(x_i)}$ (sigma-X). Take defect counts 0, 1, and 2 with probabilities $0.5$, $0.3$, and $0.2$, which have mean $\mu_X = 0.7$ (mu-X, the mean of X). The weighted squared deviations are $(0-0.7)^2(0.5) = 0.245$, $(1-0.7)^2(0.3) = 0.027$, and $(2-0.7)^2(0.2) = 0.338$, and they sum to the variance $0.610$. Taking the square root gives $\sigma_X = \sqrt{0.610} \approx 0.781$ defects.