# Gini coefficient and Lorenz curve explained

Gini coefficient and Lorenz curve explainedLet us understand one of the important concepts that we keep hearing about, read on to know what and why of Gini and all about Lorenz curve:)JuhiBlockedUnblockFollowFollowingMar 6This post will explain the Gini coefficient’s usage and relevance for the data science professionals and we will also understand the Lorenz curve which is a way to determine Gini coefficient graphically.

What is the traditional definition of Gini index?The Gini index or Gini coefficient is a statistical measure of distribution which was developed by the Italian statistician Corrado Gini in 1912.

It is used as a gauge of economic inequality, measuring income distribution among a population.

The coefficient ranges from 0 (or 0%) to 1 (or 100%), with 0 representing perfect equality and 1 representing perfect inequality.

Values over 1 are not practically possible as we don’t take into account the negative incomes.

(Income can be 0 at its lowest but not negative)Thus, a country in which every resident has the same income would have an income Gini coefficient of 0.

A country in which one resident earned all the income, while everyone else earned nothing, would have an income Gini coefficient of 1.

As we know now, the Gini coefficient is an important tool for analyzing income or wealth distribution within a country or region, but,Gini should not be mistaken for an absolute measurement of income or wealth.

A high-income country and a low-income one can have the same Gini coefficient, as long as incomes are distributed similarly within each country:Turkey and the U.

S.

both had income Gini coefficients around 0.

39–0.

40 in 2016, according to the OECD, though Turkey’s GDP per person was less than half of the U.

S.

’s (in 2010 dollar terms).

Use of Gini index in data modellingThe Gini Coefficient or Gini Index measures the inequality among the values of a variable.

Higher the value of an index, more dispersed is the data.

Alternatively, the Gini coefficient can also be calculated as the half of the relative mean absolute difference.

Graphical Representation of the Gini Index (Lorenz curve)The Gini coefficient is usually defined mathematically based on the Lorenz curve, which plots the proportion of the total income of the population (y-axis) that is cumulatively earned by the bottom x% of the population.

The line at 45 degrees thus represents perfect equality of incomes.

The Gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked A in the diagram(Titled Figure below) over the total area under the line of equality (marked A and B in the diagram ); i.

e.

, G = A / (A + B).

It is also equal to 2A and to 1–2B due to the fact that A + B = 0.

5 (since the axes scale from 0 to 1).

The Gini index is often represented graphically through the Lorenz curve, which shows income (or wealth) distribution by plotting the population percentile by income on the horizontal axis and cumulative income on the vertical axis.

The Gini coefficient is equal to the area below the line of perfect equality (0.

5 by definition) minus the area below the Lorenz curve, divided by the area below the line of perfect equality.

In other words, it is double the area between the Lorenz curve and the line of perfect equality.

Another way of thinking about the Gini coefficient is as a measure of deviation from perfect equality.

The further a Lorenz curve deviates from the perfectly equal straight line (which represents a Gini coefficient of 0), the higher the Gini coefficient and the less equal the society.

Figure: Img source-WikipediaExample: Following is an excel illustration of how Gini coefficient can be calculated by plotting the Lorenz curve and calculating the area between the equality line and the curve.

So, now the Gini coefficient and its calculation using Lorenz curve should be a a piece of cake for you guys:)Let me know if you have any questions or suggestion.

Thank you for reading:).. More details