Skewness and Kurtosis Calculator
Use this calculator to find the skewness and kurtosis of your dataset. It is designed for students, analysts, and professionals who need to determine the distribution characteristics of their data.
Data Input
Results
Data Source and Methodology
This tool uses standard statistical formulas for skewness and kurtosis calculations. All calculations are based on data and methodologies from Social Science Statistics. All calculations are based on the formulas and data provided by this source.
The Formula Explained
Skewness Formula: \( \text{Skewness} = \frac{N \sum (X_i - \bar{X})^3}{(N-1)(N-2) \cdot (\text{SD})^3} \)
Kurtosis Formula: \( \text{Kurtosis} = \frac{N(N+1) \sum (X_i - \bar{X})^4}{(N-1)(N-2)(N-3) \cdot (\text{SD})^4} - \frac{3(N-1)^2}{(N-2)(N-3)} \)
Glossary of Variables
- Xi: Each value in the data set
- \(\bar{X}\): Mean of the data set
- N: Number of values in the data set
- SD: Standard deviation of the data set
How It Works: A Step-by-Step Example
For a data set 3, 7, 8, 5, 12, 14, 21, 13, 18, the skewness and kurtosis are calculated using the formulas provided above. The mean of this data set is 11.2, and the standard deviation is 5.76. Using these values, the skewness and kurtosis can be computed as shown in the formula section.
Frequently Asked Questions (FAQ)
What is skewness?
Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.
What is kurtosis?
Kurtosis is a measure of the tails' heaviness of the probability distribution of a real-valued random variable.
Why calculate skewness and kurtosis?
Understanding skewness and kurtosis helps in identifying the nature and characteristics of the distribution of your data.
How do I interpret skewness?
A positive skew indicates a distribution with an asymmetric tail extending towards more positive values.
How do I interpret kurtosis?
High kurtosis in a data set is an indicator that data has heavy tails or outliers.