Calculadora de Assimetria e Curtose (5 valores)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
sk = E[((x−μ)/σ)³] ; ku = E[((x−μ)/σ)⁴] − 3
About this calculator
This calculator analyzes skewness and kurtosis of a dataset using five values: minimum, first quartile, median, third quartile, and maximum. Skewness measures distribution asymmetry: positive values indicate right tail, negative left tail. Kurtosis measures tail 'heaviness' relative to normal distribution: positive (leptokurtic) indicates heavier tails, negative (platykurtic) lighter tails. It uses formulas based on quartiles and median to estimate these moments, useful for quick exploratory analysis without raw data.
How it works: The five values summarize the distribution. Skewness is estimated by Bowley's formula: (Q3 + Q1 - 2*Median) / (Q3 - Q1). Kurtosis is estimated by Moors' formula: (Q3 - Q1) / (2*(P90 - P10)), where P90 and P10 are approximated from extremes. These dimensionless measures allow shape comparison across distributions. Results are displayed in a table with textual interpretation (e.g., 'Positive skewness: tail to the right').
When to use: Ideal for preliminary analysis of financial data (stock returns), quality control (measurement distributions), or any situation needing quick symmetry and concentration checks. Useful for comparing distributions across samples without full datasets. Caution: estimates from five values are approximate and less precise than sample moments from all data.
Frequently asked questions
What does positive skewness mean?
Positive skewness means the right tail is longer than the left, indicating high extreme values. The median is typically left of the mean.
What is the difference between kurtosis and variance?
Variance measures total dispersion; kurtosis measures tail and peak heaviness, describing shape beyond dispersion.
Can I use this calculator with non-numeric data?
No, data must be numeric and at least interval scale for quartiles and median to be meaningful.
What does negative kurtosis mean?
Negative kurtosis (platykurtic) indicates lighter tails and a flatter peak than normal, meaning fewer extreme outliers.
Are results accurate for small samples?
With only five values, accuracy is limited. For small samples, use all raw data with traditional skewness and kurtosis formulas.