Mathematics and Statistics · Ch 12 — Skewness
Interpreting and Comparing Skewness
Interpreting and Comparing Skewness
Both coefficients are relative measures — pure numbers — and are read the same way regardless of the data's units.
| Value of coefficient | Shape of distribution | Longer tail | Order of averages |
|---|---|---|---|
| Equal to | Symmetric | none | Mean = Median = Mode |
| Greater than | Positively skewed | right | Mean > Median > Mode |
| Less than | Negatively skewed | left | Mean < Median < Mode |
The size of the number (ignoring its sign) tells the degree: the closer it is to the more nearly symmetric the distribution, and the closer to its limit (, practically , for Karl Pearson's; for Bowley's) the more strongly skewed it is. A coefficient of describes a distribution far more skewed than one of , and the positive sign in each case fixes the direction as right-tailed.
Because both coefficients are dimensionless, they let an analyst compare the skewness of two different distributions even when the raw data are measured in different units or on different scales — which is the whole practical purpose of a relative measure. When comparing, keep the two coefficients separate: report a Karl Pearson value against another Karl Pearson value, and a Bowley value against another Bowley value, since the two methods use different parts of the data and are not on the same numerical scale. …
A measure of skewness expressed as a pure number, free of the units of the data, so that the skewness of two distributions can be compared directly; both Karl Pearson's and Bowley's co …