## Definition The ==Standard Deviation (SD)== is the positive square root of the variance, providing a measure of spread in the same units as the random variable itself: $ \text{SD}(X) = \sigma = \sqrt{\text{Var}(X)} $ > [!example]- If the variance of a loss distribution is 400, what is the standard deviation and what does it mean? > $ \sigma = \sqrt{400} = 20 $ > This means that, on average, individual loss values deviate about 20 units from the mean loss. Because the standard deviation shares units with the original variable (unlike variance, which is in squared units), it is more directly interpretable.