Skewness Calculator

Pearson's Coefficient

SK = 3(Mean - Median)/Standard Deviation

• Simple and intuitive measure
• Based on central tendency
• Robust to outliers
• Range: typically -3 to +3
• Zero indicates symmetry

Sample Skewness

g₁ = [n/(n-1)(n-2)] Σ[(x-μ)³/σ³]

• Moment-based measure
• Adjusts for sample size
• More sensitive to outliers
• Unbiased estimator
• Used in small samples

Population Skewness

γ₁ = E[(X-μ)³]/σ³

• Third standardized moment
• No bias correction
• Theoretical measure
• Used in large samples
• Distribution properties

Positive Skewness

• Right-tailed distribution
• Mean > Median > Mode
• Longer right tail
• Common in income data
• Asset returns
• Response times

Negative Skewness

• Left-tailed distribution
• Mean < Median < Mode
• Longer left tail
• Exam scores
• Age distributions
• Quality measures

Symmetric Distribution

• Zero skewness
• Mean = Median = Mode
• Normal distribution
• Equal tails
• Bell curve shape

Financial Analysis

• Return distributions
• Risk assessment
• Portfolio analysis
• Option pricing
• Market indicators

Quality Control

• Process capability
• Defect analysis
• Measurement systems
• Control charts
• Specification limits

Research Methods

• Data screening
• Assumption testing
• Distribution fitting
• Outlier detection
• Transformation selection