The standard deviation is the positive square root of the variance. The variance is the expected value of the squared deviations around the expected value, weighted by the probability of each observation. The expected value is: (0.5) × (0.12) + (0.3) × (0.1) + (0.2) × (0.15) = 0.12. The variance is: (0.5) × (0.12 − 0.12)2 + (0.3) × (0.1 − 0.12)2 + (0.2) × (0.15 − 0.12)2 = 0.0003. The standard deviation is the square root of 0.0003 = 0.017 or 1.7%.
