Skewness Calculator
Skewness Analysis
Data Values
Related Calculators
Understanding Skewness
Skewness Definition
Skewness measures the asymmetry of a probability distribution. Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values, while negative skewness indicates a tail extending toward more negative values.
Key Formula:
Skewness = Σ[(Xᵢ - μ)³] / (n × σ³)
Where μ is mean, σ is standard deviation, n is sample size
Skewness Interpretation
A skewness of 0 indicates a perfectly symmetric distribution. Values between -0.5 and 0.5 are considered approximately symmetric. Values beyond ±1 indicate highly skewed distributions.
Visual Interpretation:
- • Leptokurtic (K > 3): Flat-topped distribution with heavy tails
- • Mesokurtic (K ≈ 3): Normal-like distribution with moderate tails
- • Platykurtic (K < 3): Light-tailed distribution with flat top
- • Normal (K = 3): Bell-shaped distribution with moderate tails
How to Use Skewness Calculator
Step-by-Step Instructions
- 1.Enter Data Values: Input your dataset values in the textarea, separated by commas (e.g., "1, 2, 3, 4, 5").
- 2.Minimum Sample Size: Ensure you have at least 3 data points for meaningful skewness calculation.
- 3.Calculate Skewness: Click the "Calculate Skewness" button to perform the analysis.
- 4.Review Results: Examine the skewness value and interpretation to understand your distribution's asymmetry.
- 5.Compare Statistics: Review mean, median, and mode to understand the relationship between central tendency measures.
Data Requirements
Minimum 3 data points required. Larger samples provide more reliable skewness estimates. Avoid datasets with all identical values.
Best Practices
Check for outliers, consider data transformation for highly skewed data, and use skewness with other statistics for complete analysis.
Skewness Formulas
Pearson's Moment Coefficient
Skewness = Σ[(Xᵢ - μ)³] / (n × σ³)
The most common measure of skewness, based on the third standardized moment
Sample Skewness (Unbiased)
g₁ = √[n(n-1)]/(n-2) × Σ[(Xᵢ - μ)³] / (n × σ³)
Adjusted version that provides unbiased estimates for small samples
Pearson's First Coefficient
Skewness = (Mean - Mode) / Standard Deviation
Simpler measure using the relationship between mean, mode, and standard deviation
Alternative Measures
Median Skewness: (3(Mean - Median)) / Standard Deviation
Robust alternative less affected by outliers
Skewness Applications
Financial Analysis
- • Investment Returns: Assess asymmetry in return distributions to evaluate investment risk
- • Portfolio Management: Identify non-normal return patterns affecting portfolio optimization
- • Risk Assessment: Evaluate downside risk and potential for extreme losses
- • Asset Pricing: Model expected returns considering distribution asymmetry
Data Science
- • Data Preprocessing: Identify need for data transformation to achieve normality
- • Machine Learning: Assess feature distribution assumptions for algorithms
- • Anomaly Detection: Identify unusual patterns in data distributions
- • Quality Control: Monitor process performance and detect shifts in distributions
Research & Analysis
- • Biological Studies: Analyze growth patterns and population distributions
- • Social Sciences: Examine income distribution, survey responses, and demographic data
- • Environmental Science: Study pollution levels and natural phenomena distributions
- • Quality Assurance: Monitor manufacturing processes and product specifications
Frequently Asked Questions
What does positive skewness indicate?
Positive skewness indicates that the distribution has a longer tail on the right side. This means there are more extreme positive values, and the mean is typically greater than the median.
How do I interpret skewness values?
Values between -0.5 and 0.5 indicate approximately symmetric distributions. Values between ±0.5 and ±1 indicate moderate skewness. Values beyond ±1 indicate highly skewed distributions.
Why is skewness important in data analysis?
Skewness affects statistical tests, machine learning algorithms, and data visualization. It helps identify the need for data transformation and informs appropriate analytical methods.
How does skewness relate to mean and median?
In positively skewed distributions, mean > median > mode. In negatively skewed distributions, mean < median < mode. In symmetric distributions, mean = median = mode.
Conclusion
Skewness analysis provides essential insights into distribution asymmetry, helping identify patterns, outliers, and data characteristics that affect statistical analysis and decision-making. This calculator offers comprehensive skewness calculation including mean, median, mode, and interpretation to support data analysis across finance, science, and research applications.