What Is a Skewness Calculator?

A skewness calculator measures the asymmetry of a probability distribution using three methods: population skewness (γ₁), Fisher's sample skewness (G₁), and Pearson's second skewness coefficient. Pre-filled with a left-skewed dataset, the calculator shows numerical skewness values, an interpretation, and a histogram visualizing the distribution shape.

Understanding Skewness Values

Skewness = 0: perfectly symmetric. Positive skewness: the right tail is longer — most values cluster at the left (e.g., income distributions). Negative skewness: the left tail is longer — most values cluster at the right (e.g., exam scores on an easy test). Magnitude matters: |skew| < 0.5 is approximately symmetric, 0.5–1.0 is moderate, and >1.0 is highly skewed.

Population vs Sample Skewness

Population skewness assumes you have the entire population: γ₁ = m₃/σ³. Sample skewness (Fisher's G₁) adjusts for bias using: G₁ = [n/((n−1)(n−2))] × Σ((xᵢ−x̄)/s)³. For large samples, both converge. For small samples, Fisher's adjustment is important — population skewness underestimates the true skewness of small samples.

Skewness in Finance

Financial returns often exhibit negative skewness — occasional large losses (crashes) with more frequent small gains. Investors dislike negative skewness because it implies tail risk. The 2008 crash was a negative skew event. Options pricing models that assume zero skewness (like Black-Scholes) misprice tail risk. Skewness is the third moment of the distribution — after mean (1st) and variance (2nd).

Correcting Skewness

Many statistical tests assume normality (symmetric, zero skewness). If data is skewed: log transform (right skew), square root (moderate right skew), reciprocal (strong right skew), or Box-Cox (automatic power selection). After transformation, verify that skewness is closer to zero. Some modern methods (bootstrap, permutation tests) work without normality assumptions.