SKEWNESS

The second central moment, variance, tells us how spread-out a random variable is around the mean. The third central moment tells us how symmetrical the distribution is around the mean. Rather than working with the third central moment directly, by convention we first standardize the statistic. This standardized third central moment is known as skewness:

(3.41)

where s is the standard deviation of X.

By standardizing the central moment, it is much easier to compare two random variables. Multiplying a random variable by a constant will not change the skewness.

A random variable that is symmetrical about its mean will have zero skewness. If the skewness of the random variable is positive, we say that the random variable exhibits positive skew. Figures 3.1 and 3.2 show examples of positive and negative skewness.