The ________ of a random variable X, denoted σX, is simply the square root of the variance

The ________ of a random variable X, denoted σX, is simply the square root of the variance

• A. Variance
• B. Standard deviation
• C. Mean
• D. Skewness

Answer: (B)

Standard deviation is the measure of how spread out a random variable is around its mean. It is defined as the square root of the variance: σX = sqrt(Var(X)). The variance captures the average squared deviation from the mean, which ends up in squared units, making interpretation harder. Taking the square root brings it back to the same units as X, giving a intuitive sense of typical deviation. The variance itself is Var(X), the mean is the expected value, and skewness describes asymmetry in the distribution. So the square root of the variance is the standard deviation, denoted σX.

Standard deviation is the measure of how spread out a random variable is around its mean. It is defined as the square root of the variance: σX = sqrt(Var(X)). The variance captures the average squared deviation from the mean, which ends up in squared units, making interpretation harder. Taking the square root brings it back to the same units as X, giving a intuitive sense of typical deviation. The variance itself is Var(X), the mean is the expected value, and skewness describes asymmetry in the distribution. So the square root of the variance is the standard deviation, denoted σX.