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Also known as: Asymmetry
A numerical measure of the asymmetry of a probability distribution around its mean.
DESCRIPTION
Skewness quantifies how much a distribution’s tail extends more to one side than the other. Positive skew indicates a longer right tail; negative skew indicates a longer left tail. Skewness influences statistical tests, confidence intervals, and model assumptions. Practitioners often mitigate skew with transformations (e.g., log, Box–Cox) before modeling. Understanding skewness helps diagnose outliers, non-normality, and appropriate summary statistics.
ALTERNATIVE DEFINITIONS
Wikipedia
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.
Provides the formal statistical framing around the mean.
NIST/SEMATECH e-Handbook of Statistical Methods
Skewness is a measure of symmetry, or more precisely, the lack of symmetry.
Highlights skewness as a deviation from symmetry rather than absolute direction.
RELATED TERMS
Kurtosis Mean Median Variance Normal Distribution Outliers Transformation Log Transform Z-score Probability Distribution
COMPETING TERMS
Symmetric Distribution
KNOWLEDGE AREAS
Mathematics Data Science Data Quality
TARGET AUDIENCE
Data Scientist Data Analyst Data Steward
EXTERNAL SOURCES
- Wikipedia - Skewness
- NIST - Authoritative statistical reference on skewness
- Wolfram MathWorld - Formulas and properties of skewness
TOP QUESTIONS
Why does Skewness matter in modeling?
Skewed distributions can violate model assumptions and bias parameter estimates. Transformations or robust methods often improve fit and interpretability.
Category: Relevancy
How do I interpret positive Skewness?
A positive value indicates a long right tail; mean exceeds median. Income distributions often exhibit positive skew.
Category: Interpretation
What is a common mistake with Skewness?
Confusing skewness with kurtosis. Skewness indicates asymmetry; kurtosis reflects tail heaviness and peakedness.
Category: Mistakes
How can I reduce Skewness?
Apply transformations like log, square root, or Box–Cox, and reassess distributional assumptions.
Category: BestPractices
Is Skewness robust to outliers?
No, it’s sensitive to outliers. Consider robust measures or trimming when outliers dominate.
Category: Risk
How does Skewness affect hypothesis testing?
Non-normality may inflate Type I/II errors for tests assuming normality. Use non-parametric tests when appropriate.
Category: Testing
What sample size is needed to trust Skewness estimates?
Larger samples yield more stable estimates; small samples can give misleading skewness values.
Category: Requirements
Can Skewness be zero for non-normal distributions?
Yes. A distribution can be symmetric yet non-normal; zero skewness doesn’t imply normality.
Category: Misunderstanding
How is Skewness computed?
Common formulas use the third standardized moment, with bias corrections for sample estimates.
Category: Basics