Coefficient of Skewness Calculator
Measure how lopsided your data is — the moment coefficient of skewness plus Pearson’s median-based skewness from a list of values.
How it works
g₁ = m₃ ÷ m₂^(3/2) · m_k = (1/n)·Σ(x−x̄)ᵏ · Pearson = 3(x̄ − median) ÷ s
Skewness measures asymmetry. The moment coefficient g₁ divides the third central moment by the standard deviation cubed, so it is dimensionless: positive values mean a longer right tail, negative a longer left tail, and zero a symmetric shape. The adjusted Fisher–Pearson G₁ corrects g₁ for sample bias, while Pearson’s median-based measure gives a quick, outlier-robust alternative built from the gap between the mean and the median.
Worked example
For 12, 15, 17, 20, 22, 25, 34, 41 the mean is 23.25 and the median is 21. The mean sits above the median, so the data is pulled right by the large 34 and 41 — g₁ comes out positive, confirming a right-skewed distribution.
Sources: Skewness — Wikipedia
Frequently asked questions
What is considered a large skew?
A rough rule of thumb: |skewness| under 0.5 is fairly symmetric, 0.5–1 is moderately skewed, and above 1 is highly skewed. These are guidelines, not hard cutoffs — always look at a histogram too.
Why do the three skewness numbers differ?
They estimate the same idea with different formulas. g₁ and G₁ use the cubed deviations (G₁ adds a small-sample correction), while Pearson’s version uses the mean-minus-median gap, which reacts less to extreme outliers. On symmetric data all three sit near zero.
Does skewness need a normal distribution?
No — skewness describes any distribution’s asymmetry. It is often used precisely to check how far data departs from the perfectly symmetric normal curve before running tests that assume normality.
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For education — check the assumptions (sample size, distribution shape) before using statistics in real decisions.