Measure the asymmetry and direction of a distribution's tail.
Last updated: March 2026
Skewness measures the asymmetry of a statistical distribution—whether data is balanced around its center or lopsided. A symmetric distribution (like normal distribution) has skewness near 0. Right-skewed (positive skewness) has a tail extending to the right, meaning some extremely high values pull the mean above the median. Left-skewed (negative skewness) has a tail extending left, with extreme low values below the median.
Skewness is crucial in finance, sociology, and science. Income distributions are typically right-skewed (few very rich people). Test scores might be left-skewed if most students do well. Understanding skewness helps identify outliers, choose appropriate statistical tests, and interpret data accurately.
This calculator provides three skewness measures: sample skewness (g₁), adjusted skewness (G₁, preferred for small samples), and Pearson's 2nd coefficient. Interpretation: |skewness| < 0.5 is approximately symmetric, > 1 is highly skewed.
Income Distribution: Symmetric vs Right-Skewed
Skewness indicates whether data is symmetric or asymmetric. This affects interpretation of mean vs. median, choice of statistical tests, and confidence intervals. Highly skewed data may require transformation before analysis.
g₁ (sample skewness) is biased. G₁ (adjusted skewness) is unbiased and better for small samples. For large samples (n > 100), they're nearly identical. Prefer G₁ for inference.
Yes! Skewness can range from −3 to +3 theoretically, though extreme values are rare. |Skewness| > 1 indicates highly asymmetric distribution. Most real data has |skewness| < 2.
Positive (right-skewed): tail extends right, mean > median, extreme high values. Example: income. Negative (left-skewed): tail extends left, mean < median, extreme low values. Example: test scores when most pass.
Different measures! Skewness measures asymmetry direction. Kurtosis measures tail weight (how extreme outliers are). You can have symmetric data with high kurtosis (Cauchy distribution).
Options: (1) Use non-parametric tests, (2) Transform data (log, square root), (3) Use robust statistics (median instead of mean), (4) Report median with skewness value to explain why.
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