Skewness Calculator
Enter numeric values to compute the sample skewness and supporting statistics using the Fisher-Pearson estimator.
Count
8
Mean
25.8750
Std. deviation
15.0375
Skewness
1.9742
Interpretation: Positively skewed (longer right tail).
How to Use This Calculator
- Enter numeric observations using spaces or commas.
- Review the calculated mean, standard deviation, and skewness.
- Interpret skewness to understand distribution asymmetry.
- Combine skewness with visual plots or kurtosis for further insight.
Formulas
Sample skewness (Fisher-Pearson) = [n / ((n − 1)(n − 2))] × Σ((x − μ)³) / s³
μ is the sample mean, s is the sample standard deviation, and n is the sample size.
Standard deviation uses the unbiased estimator: s = √(Σ(x − μ)² / (n − 1)).
This bias-adjusted sample skewness matches the implementation used in many statistical packages.
Frequently Asked Questions
What skewness value indicates symmetry?
Values near zero (for example between −0.5 and 0.5) suggest an approximately symmetric distribution.
Can skewness be undefined?
When the standard deviation is zero (all values identical), skewness is undefined. The calculator reports zero with a note.
Do outliers influence skewness?
Yes. Skewness is sensitive to extreme values because it uses cubed deviations.
Should I use sample or population skewness?
For sample data, use this bias-adjusted estimator. For complete populations, the adjustment factor is unnecessary.