Calculate Skewness and Kurtosis by Hand
Skewness and kurtosis are crucial statistical measures that describe the shape of a probability distribution. Calculating them by hand helps understand the underlying data distribution…
- Enter your data points, separated by commas.
- Enter the sample size (n).
- Click ‘Calculate’.
The formulas for skewness (γ1) and kurtosis (γ2) are:
| γ1 | γ2 |
|---|---|
| ∑(xi – μ)³ / n * σ³ | ∑(xi – μ)⁴ / n * σ⁴ – 3 |
| Distribution | Skewness | Kurtosis |
|---|---|---|
| Normal | 0 | 3 |
| Uniform | 0 | 1.8 |
- Skewness indicates symmetry: positive values indicate right-skewed, negative values indicate left-skewed.
- Kurtosis indicates outliers: high values indicate heavy tails, low values indicate light tails.
What is the difference between skewness and kurtosis?
Skewness describes the asymmetry of a distribution, while kurtosis describes the heaviness of the tails and the peakedness of the distribution.
For more information, see Khan Academy and Introductory Statistics.