# The Gini Coefficient

The most widely used summary measure of inequality in the distribution of household income is the Gini coefficient.

The lower its value, the more equally household income is distributed.

The Gini coefficient is a measure of the way in which different groups of households receive differing shares of total household income.

For example, the bottom 5 per cent of households might only have a 1 per cent share of total household income. The bottom 10 per cent of households might have a 3 per cent share; the bottom 20 per cent might have an 8 per cent share, and so on.

The Gini coefficient is a measure of the overall extent to which these groupings of households, from the bottom of the income distribution upwards, receive less than an equal share of income.

## How is it calculated?

The idea described above is expressed more formally by the Lorenz curve of the household income distribution, from which the Gini coefficient can be calculated.

Based on a ranking of households in order of ascending income, the Lorenz curve is a plot of the cumulative share of household income against the cumulative share of households. The curve will lie somewhere between two extremes.

Complete equality, where income is shared equally among all households, results in a Lorenz curve represented by a straight line.

The opposite extreme, complete inequality, where only one household has all the income and the rest have none, is represented by a Lorenz curve which comprises the horizontal axis and the right-hand vertical axis.

The Gini coefficient is the area between the Lorenz curve of the income distribution and the diagonal line of complete equality, expressed as a proportion of the triangular area between the curves of complete equality and inequality.

It can be seen that complete equality would result in a Gini coefficient of zero, and complete inequality, a Gini coefficient of 100.

All the Gini coefficients shown in 'The effects of taxes and benefits on household income' are based on distributions of equivalised household income.

Equivalisation is a standard methodology that takes into account the size and composition of households and adjusts their incomes to recognise differing demands on resources.

## How is it used?

The Gini coefficient is used to show the degree of income inequality between different groups of households in the population.

It can also be used to show how inequality of incomes has been changing over a period of time.

Content from the Office for National Statistics.
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