# Measures of Inequality

## Measures of Inequality

#### Measures of Inequality

Here are a few of the common measures of inequality, how they are calculated, and what they mean:

The Range is simply the difference in wealth between the richest household and the poorest household.

The Gini Coefficient is the most commonly used measure of inequality of income or wealth. It equals 0 in a perfectly equal society (every household has the same amount of wealth) and 1 in a society of perfect inequality (one household owns all the wealth and everyone else has none).

For comparison, here is the Gini coefficient (for wealth) in 2000 for several countries:

Country Gini Coefficent
Japan 0.547 (country with lowest value)
China 0.550
Italy 0.609
Australia 0.622
Norway 0.633
India 0.669
United Kingdom 0.697
Russia 0.699
Sweden 0.742
Mexico 0.749
United States 0.801
Namibia 0.847 (country with highest value)

When there is an immense amount of debt (as we’ll see later), the Gini coefficient can be larger than 1. Note that the Chancy Islands model calculates the index using an array formula.

The Hoover Index, also known as the Robin Hood Index, is the portion of the total community wealth that would have to be redistributed (taken from the richer half of the population and given to the poorer half) to achieve wealth uniformity. Like the Gini Coefficient, it equals 0 in a perfectly equal society and 1 in a society of perfect inequality. In a society with immense debt, it can also be larger than 1.

The coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion and is defined as the ratio of the standard deviation to the mean (average). A value of 0 means that every value is the same (every household has the same wealth). Values greater than about 0.3 mean that the level of wealth varies widely.

The Quartile Coefficient of Dispersion compares the wealth of households at the third quartile (Q3), that is, at the 75th percentile (75% of the households have less wealth than this household), to those at the first quartile (Q1 = 25th percentile). It is calculated by dividing the difference (Q3–Q1) by the sum (Q3+Q1).

The Decile Coefficient of Dispersion compares the wealth of households at the 9th decile (D9 = 90th percentile) with those at the 1st percentile (D1 = 10th percentile). It is calculated by dividing the difference (D9–D1) by the sum (D9+D1).

The 20:20 Ratio compares the total wealth held by the richest 20% of households to the total wealth held by the poorest 20%. This measure, and the Palma Ratio below, specifically measure the division between the rich and poor.

The Palma Ratio compares the total wealth held by the richest 10% of households to the total wealth held by the poorest 40%.