Sample Skewness Calculator
Sample skewness summarizes distribution asymmetry. The adjusted Fisher–Pearson estimator corrects the basic third standardized moment for sample size.
How to use this calculator
- Enter at least three numeric sample observations separated by semicolons.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by sample skewness calculator calculator
Adjusted skewness = √(n(n−1)) ÷ (n−2) × m₃ ÷ m₂^(3/2), where m₂ and m₃ are sample central moments with divisor n.
- Adjusted skewness = √(n(n−1)) ÷ (n−2) × m₃ ÷ m₂^(3/2), where m₂ and m₃ are sample central moments with divisor n.
- Skewness is sensitive to extreme values and noisy in small samples. Inspect a histogram or robust summaries as well.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
The values 2; 4; 5; 7; 12; 13 form a positively skewed sample.
The calculator computes the sample mean, central moments and adjusted skewness.
Positive skewness indicates a longer or heavier right tail in this sample summary.
Understanding the result
Sample skewness summarizes distribution asymmetry. The adjusted Fisher–Pearson estimator corrects the basic third standardized moment for sample size.
Skewness is sensitive to extreme values and noisy in small samples. Inspect a histogram or robust summaries as well.
Important notes
Skewness is sensitive to extreme values and noisy in small samples. Inspect a histogram or robust summaries as well.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
Can skewness be negative?
Yes. Negative skewness indicates left-skew in the selected convention.
Does skewness prove a distribution is normal?
No. It only describes one aspect of shape.
How should I interpret this result?
Skewness is sensitive to extreme values and noisy in small samples. Inspect a histogram or robust summaries as well.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.