Statistical Inference: A Short Course

3.8 Skewness

We may view the notion of skewness as a departure from symmetry.³ Suppose we have a sample of X values. Then if the distribution of X is symmetrical, = med = mo (Fig. 3.5). If the distribution is skewed to the right or positively skewed (its right-hand tail is elongated) the > med > mo. And if the distribution is skewed to the left or negatively skewed (its left-hand tail is elongated), then < med < mo.

Figure 3.5 Comparing the relative positions of the mean, median, and mode.

Can we measure skewness? While there are a few different methods for detecting skewness in a data set, one measure, which is particularly easy to apply, is the Pearson Coefficient of Skewness:

(3.10a)

(3.10b)

Here each of these coefficients of skewness is a pure number (independent of units) and serves as an index of the degree of skewness. So if, for instance, sk = 0, the distribution is symmetrical; ...