The English statistician Karl Pearson (1857–1936) introduced a formula for the skewness of a distribution.

P = 3(x̅ - median)/s     Pearson’s index of skewness

Most distributions have an index of skewness between -3 and 3. When P > 0, the data are skewed right. When P < 0, the data are skewed left. When P = 0, the data are symmetric. Calculate the coefficient of skewness for each distribution. Describe the shape of each.

(a) x̅ = 17, s = 2.3, median = 19

(b) x̅ = 32, s = 5.1, median = 25

(c) x̅ = 9.2, s = 1.8, median = 9.2

(d) x̅ = 42, s = 6.0, median = 40