• Comparing distributions poses the problem of choosing appropriate metrics
• Ideally, we would like an index that ranks distributions according to appropriate distributional values
• However no single index can fully summarize a distribution
• The median and mean fail to show the degree of equality of distributions (the median would remain unchanged even if everyone with income below the median had their income reduced by half. The mean would remain unchanged if we were to take money from the poorest and give it to the richest.
• A commonly used distributional measure is the Gini Index of relative inequality, which is related to the Lorenz Curve
• A Lorenz curve is constructed by ranking the population by income and asking: What percent of the income goes to the poorest X percent of the population? With the percentage of income measured on the vertical axis and the percentage of population measured on the horizontal axis, the income distribution will trace out a curve going for the origin to the point representing 100 percent of the income going to 100 percent of the population
• The Gini coefficient provides an attractive measure of comparing the equality of distributions over the entire range of income.
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