“The Gini coefficient is a statistical measure ranging from 0 to 1 (or 0 to 100) that quantifies income or wealth inequality within a population. A coefficient of 0 indicates perfect equality, while 1 represents maximum inequality. It is calculated using the Lorenz curve, which graphs cumulative income against population share.” – Gini coefficient
The Gini coefficient is a widely used statistical measure that quantifies the degree of inequality in the distribution of income or wealth within a population. Ranging from 0 to 1 (or 0 to 100 when expressed as a percentage), a value of 0 represents perfect equality where everyone has the same income, while 1 indicates maximum inequality where one individual holds all the income.1,2,3
It derives from the Lorenz curve, a graphical representation plotting the cumulative proportion of income (or wealth) against the cumulative proportion of the population, ordered from poorest to richest. The line of perfect equality is a 45-degree diagonal, and the Gini coefficient is calculated as the ratio of area A (between the Lorenz curve and the line of equality) to the total area under the line of equality (A + B), simplifying to G = A / (A + B) or, since A + B = 0.5, G = 2A = 1 – 2B.1,2,3,6
Mathematical Formulation
For discrete data with incomes y_i ordered from smallest to largest, the Gini coefficient is:
G = \frac{1}{n} \left( n + 1 - 2 \frac{\sum_{i=1}^n (n + 1 - i) y_i}{\sum_{i=1}^n y_i} \right)3
Alternatively, it equals half the relative mean absolute difference:
G = \frac{1}{2 \mu} \sum_{i=1}^n \sum_{j=1}^n f(y_i) f(y_j) |y_i - y_j|,
where \mu is the mean and f(y_i) are probabilities.2,3,4
For continuous distributions with cumulative function F(y), it integrates over absolute differences.2,3
Applications and Interpretation
Commonly applied to income data by organisations like the World Bank, the coefficient helps compare inequality across countries or over time. Higher granularity in data yields more precise estimates, though it remains sensitive to population size and measurement scale.2,7
Corrado Gini: The Theorist Behind the Measure
The most directly associated theorist is **Corrado Gini** (1884-1965), the Italian statistician and sociologist who invented the coefficient. Published in his 1912 paper Variabilità e mutabilità (Variability and Mutability), Gini introduced it as a tool to measure statistical dispersion, initially for any distribution but soon applied to income inequality.2
Born in Friuli, Italy, Gini studied mathematics at the University of Bologna, earning a degree in 1905. He shifted to statistics and sociology, founding the Italian school of biotypology-a controversial eugenics-influenced theory classifying humans by physical and psychological types. Appointed professor at the University of Cagliari (1913) and later Padua, he directed Italy’s Central Statistical Institute (1926-1932) under Mussolini, influencing fascist policies on demographics and economics, which tarnished his later reputation.
Gini pioneered sociometry and index numbers, but his inequality measure endures as his legacy, adopted globally despite his political ties. Post-WWII, he continued academic work until his death in 1965.2
References
1. https://goodcalculators.com/gini-coefficient-calculator/
2. https://www3.nccu.edu.tw/~jthuang/Gini.pdf
3. https://en.wikipedia.org/wiki/Gini_coefficient
4. https://www.statsdirect.com/help/nonparametric_methods/gini.htm
5. https://www.youtube.com/watch?v=a5EEJMZKz9I
7. https://databank.worldbank.org/metadataglossary/gender-statistics/series/SI.POV.GINI
8. https://www.youtube.com/watch?v=OUN93JwBAY4
9. https://www.jstor.org/stable/1924845
