Statistics · Ch 5 — Skewness of Frequency Distribution
Comparing Karl Pearson's and Bowley's Measures
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Comparing Karl Pearson's and Bowley's Measures
Both coefficients answer the same question — is the distribution symmetric, and if not, in which direction and to what degree — but they use different information and are not expected to give numerically identical values for the same data, only the same sign (direction) for a genuinely skewed distribution.
| Basis | Karl Pearson's Coefficient | Bowley's Coefficient |
|---|---|---|
| Uses | Mean, Mode (or Median), Standard Deviation | , Median, only |
| Uses every observation? | Yes (mean and SD use every value) | No (depends only on the middle 50% of the data) |
| Affected by extreme values | Yes, strongly (mean and SD are both sensitive to outliers) | Only mildly — quartiles ignore the extreme 25% on each side |
| Works with open-end classes | No — mean/SD cannot be computed | Yes — quartiles can still be located |
| Range | Theoretically to (practically to ) | Always to |
| Computational effort | Higher (needs SD) | Lower (needs only quartiles) |