Pearson’s Second Skewness Coefficient Using the Mean and Median

Summary

The document identifies an alternative low-moment measure of skewness as Pearson’s second skewness coefficient. It compares the sample mean with the median and scales that difference by standard deviation, giving a compact measure based on location and dispersion rather than the third central moment.

The cited statistical reference is Yule and Kendall’s textbook, which attributes the measure to Pearson. The answer states that it is zero for symmetric distributions and lies between negative three and positive three. The material is a brief identification and provenance note, not a derivation or empirical comparison. It does not discuss estimator behavior in small samples, robustness to outliers, or when this measure is preferable to conventional moment skewness.

Key ideas

• Pearson’s second skewness coefficient uses the difference between the mean and median.
• The measure scales the mean-median difference by standard deviation.
• It is zero for symmetric distributions and is described as bounded between negative three and positive three.
• The cited source is Yule and Kendall’s introductory statistics text.

Tags

# Alternative low-moment measure of skewness


# Alternative low-moment measure of skewness












$$ \widehat{\text {Skew}}_{i, t}=\frac{3 \cdot\left[\hat{\mu}_{i, t}-\operatorname{median}\left(r_{i, d, t}\right)\right]}{\hat{\sigma}_{i, t}} $$

is called Low Moment Skewness by Baltas and Salinas (2019) who don't give a citation for this alternative measure of skewness. What is its source, or where else is it used?

Others call it the Pearson 2 skewness coefficent.

## Answer by develarist (score 1, accepted)

https://quant.stackexchange.com/a/59412

Pearson 2 skewness, which compares mean and median, lying between $-3$ and $3$ while being zero for symmetric distributions, was introduced by

> Yule, G. U. and Kendall, M. G. (1950), An Introduction to the Theory of Statistics, 3rd edition, Harper Publishing Company, 162-163.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.