How this calculator works
Moment skewness standardises the third central moment using population-divisor moments. The adjusted Fisher-Pearson coefficient corrects that quantity for sample size and requires at least three observations. Pearson second skewness compares mean and median using sample SD. Bowley compares distances around the median between linear-interpolated quartiles. Constant data make standardised skewness undefined; Bowley additionally needs nonzero IQR.
Formula
m_k = Σ(x - mean)^k/n; g1 = m3/m2^(3/2); G1 = sqrt(n(n - 1))/(n - 2) × g1. Pearson2 = 3(mean - median)/s; Bowley = (Q3 + Q1 - 2median)/(Q3 - Q1).
Worked example
For 0, 0, 3, mean is 1, m2 = 2 and m3 = 2. Moment skewness is 1/sqrt(2), while adjusted skewness is sqrt(3).
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Frequently asked questions
What does positive skewness suggest?
It usually indicates a longer or more influential right tail under the selected definition. Multimodal shapes can make a simple tail interpretation misleading.
Why do methods disagree?
Moment measures use every magnitude, while Bowley uses central quartiles and Pearson compares two centres. They measure different aspects of asymmetry.
Does zero prove normality?
No. Symmetric non-normal distributions can have zero skewness. Other distributions can balance this particular coefficient without being symmetric.