## Gini coefficient |

In
**Gini coefficient** (sometimes expressed as a **Gini ratio** or a
**Gini index**) (
*jee-nee**Variability and Mutability* (
*Variabilità e mutabilità*).^{
[1]}^{
[2]}

The Gini coefficient measures the inequality among values of a
^{
[3]}^{
[4]} However, a value greater than one may occur if some persons represent negative contribution to the total (for example, having negative income or wealth). For larger groups, values close to or above 1 are very unlikely in practice. Given the normalization of both the cumulative population and the cumulative share of income used to calculate the Gini coefficient, the measure is not overly sensitive to the specifics of the income distribution, but rather only on how incomes vary relative to the other members of a population. The exception to this is in the redistribution of wealth resulting in a minimum income for all people. When the population is sorted, if their income distribution were to approximate a well-known function, then some representative values could be calculated.

The Gini coefficient was proposed by Gini as a measure of
^{
[5]} For
^{
[6]} African countries had the highest pre-tax Gini coefficients in 2008–2009, with South Africa the world's highest, variously estimated to be 0.63 to 0.7,^{
[7]}^{
[8]} although this figure drops to 0.52 after social assistance is taken into account, and drops again to 0.47 after taxation.^{
[9]} The global income Gini coefficient in 2005 has been estimated to be between 0.61 and 0.68 by various sources.^{
[10]}^{
[11]}

There are some issues in interpreting a Gini coefficient. The same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population, or with a baby boom, experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient.^{
[12]}^{
[13]}^{
[14]}

- definition
- calculation
- generalized inequality indices
- gini coefficients of income distributions
- gini coefficients of social development
- features of gini coefficient
- countries by gini index
- limitations of gini coefficient
- alternatives to gini coefficient
- relation to other statistical measures
- other uses
- see also
- references
- further reading
- external links

The Gini coefficient is usually defined
*A* in the diagram) 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 2*A* and to 1 − 2*B* due to the fact that *A* + *B* = 0.5 (since the axes scale from 0 to 1).

If all people have non-negative income (or wealth, as the case may be), the Gini coefficient can theoretically range from 0 (complete equality) to 1 (complete inequality); it is sometimes expressed as a percentage ranging between 0 and 100. In practice, both extreme values are not quite reached. If negative values are possible (such as the negative wealth of people with debts), then the Gini coefficient could theoretically be more than 1. Normally the mean (or total) is assumed positive, which rules out a Gini coefficient less than zero.

An alternative approach would be to consider the Gini coefficient as half of the
^{
[15]} The mean absolute difference is the average
*x _{i}* is the wealth or income of person

When the income (or wealth) distribution is given as a continuous
*p(x)*, where *p(x)dx* is the fraction of the population with income *x* to *x+dx*, then the Gini coefficient is again half of the relative mean absolute difference:

where μ is the mean of the distribution and the lower limits of integration may be replaced by zero when all incomes are positive.