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Pearson's Skewness Coefficients

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

((mean-mode))/sigma,

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

(3(mean-median))/sigma,

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

See also

Bowley Skewness, Pearson Mode Skewness, Skewness

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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.

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Pearson's Skewness Coefficients

Cite this as:

Weisstein, Eric W. "Pearson's Skewness Coefficients." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PearsonsSkewnessCoefficients.html

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