Pearson's Skewness Coefficients

Given a statistical distribution with measured mean, statistical median, mode, and standard deviation , Pearson's first skewness coefficient, also known as the Pearson mode skewness, is defined by

which was incorrectly implemented (with a spurious multiplicative factor of 3) in versions of the Wolfram Language prior to 6 as PearsonSkewness1[data] after loading the package Statistics`DescriptiveStatistics`.

Pearson's second coefficient is

which was implemented in versions of Wolfram Language prior to 6 as PearsonSkewness2[data].

REFERENCES:

Hildebrand, D. K. Statistical Thinking for Behavioral Scientists. Boston: Duxbury, 1986.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 101-102, 1962.