Gini Index Calculator

To calculate the Gini Index, use the Lorenz curve data to find the cumulative income share and population share. The Gini Index is determined by measuring the area under the Lorenz curve relative to a perfectly equal distribution.

The Gini Index Calculator is a tool used to measure income or wealth inequality within a population. It quantifies inequality on a scale of 0 to 1, where 0 represents perfect equality and 1 represents maximum inequality. This calculator is commonly applied in economics, statistics, and machine learning to evaluate income distributions, decision tree splits, or other inequality measures.

Formula:

Contents

1 Formula:
2 Variables:
3 Solved Calculations:
4 What is the Gini Index Calculator?

$GI = 1 – 2 \cdot \Big(1 – \frac{\sum_{i=1}^{n} (n + 1 – i) \cdot y_i}{n \cdot \sum_{i=1}^{n} y_i}\Big)$

Variables:

Variable	Description	Unit/Value
$GI$	Gini Index	Dimensionless
$y_i$	Income or value for the $i$ -th individual or group	Any measurable unit
$n$	Total number of individuals or groups	Count

Solved Calculations:

Example 1: Calculate Gini Index for a Population of 5

Step	Value	Explanation
Income Values ( $y$ )	$[10, 20, 30, 40, 50]$	Given income values
Sorted Income ( $y_i$ )	$[10, 20, 30, 40, 50]$	Sorted in ascending order
Sum of Values ( $\sum y_i$ )	$150$	Total income
Weighted Sum ( $\sum (n+1-i) \cdot y_i$ )	$450$	Weight income by position
Calculation	$GI = 1 – 2 \cdot \Big(1 – \frac{450}{5 \cdot 150}\Big)$	Substitute values into formula
Result	$GI = 0.4$	Gini Index for the population

Example 2: Calculate Gini Index for Decision Tree Splits

Step	Value	Explanation
Group 1 Values ( $y$ )	$[5, 15, 25]$	Given income values
Group 2 Values ( $y$ )	$[20, 30, 40]$	Given income values
Calculation	Compute $GI$	Apply the formula separately
Combined Gini Index	Weighted average of groups	Combine individual $GI$
Result	Example result varies	Based on given split data

What is the Gini Index Calculator?

The Gini Index Calculator is a powerful tool that is designed to measure inequality in a dataset or system. It calculates the Gini Index or Gini Coefficient, which is widely used in economics, social sciences, and machine learning. The Gini Index ranges from 0 to 1, where 0 indicates perfect equality and 1 represents maximum inequality.

This calculator allows users to input data, such as income distributions or class probabilities, and compute the Gini Index with accuracy. It is commonly used to evaluate income inequality, assess decision tree splits in machine learning, and analyze datasets through the Lorenz curve.

For example, the tool can calculate the Gini Index from data visualized in a Lorenz curve or directly from mathematical formulas.

In addition to standard calculations, the tool supports specific use cases like Gini Impurity for decision trees, weighted Gini Index for complex datasets, or country-specific comparisons of inequality.

Users can apply this calculator in tools like Excel, Python, or statistical software like R and Stata for advanced analyses.

Whether analyzing income inequality, evaluating machine learning models, or studying economic data, this calculator provides precise and reliable results.

Final Words:

All in all, the Gini Index Calculator is an essential tool for measuring inequality across various domains. It simplifies complex calculations, offering clarity and efficiency for researchers, analysts, and decision-makers.