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Mathematics and Statistics · Ch 12 — Skewness

Interpreting and Comparing Skewness

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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 coefficientShape of distributionLonger tailOrder of averages
Equal to 00SymmetricnoneMean = Median = Mode
Greater than 00Positively skewedrightMean > Median > Mode
Less than 00Negatively skewedleftMean < Median < Mode

The size of the number (ignoring its sign) tells the degree: the closer it is to 00 the more nearly symmetric the distribution, and the closer to its limit (±3\pm 3, practically ±1\pm 1, for Karl Pearson's; ±1\pm 1 for Bowley's) the more strongly skewed it is. A coefficient of +0.8+0.8 describes a distribution far more skewed than one of +0.1+0.1, 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. …

Definition 1Relative measure of skewness

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 …