A Lorenz curve is a curve that shows a probability distribution of values that have been statistically derived. They are often associated with income distributions and show inequalities. The black line of income equality represents what the distribution would actually look like if everything was equally distributed. The Lorenz curve (purple line/curve) shows the actual distribution, and shows how, income actually is, unequal and the further the curve flows away from the income equality line, the more unequal the income equality becomes.
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