How to calculate Gini coefficient

# How to calculate Gini coefficient - area for the triangles...

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How to calculate Gini coefficient Suppose we have the cumulative relative frequencies of income and households. Cumulative relative frequency of income (Y) Cumulative relative frequency of households (X) y 1 x 1 y 2 x 2 y 3 x 3 y 4 x 4 y 5 x 5 y 6 x 6 y 7 x 7 y 8 x 8 Taking the cumulative percentage of income on the vertical axis and the proportion of households on the horizontal axis, we may plot the two cumulative frequencies to obtain the Lorentz curve. A numerical measure of inequality is the Gini coefficient. It can be derived directly from the Lorentz Curve, illustrated below.

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Denoting the Gini coefficient by G , we have which must lie between 0 and 1. When there is total equality the Lorentz curve coincides with the 45º line, area A then disappears and G = 0. With total inequality (one household having all the income), area B disappears and G = 1. So the first task is to find the area B. This involves calculating the
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Unformatted text preview: area for the triangles that can be drawn by joining the each plotted points, the cumulative frequency of households associated with it, and the point of origin. Let us focus on the first triangle. The area of this red triangle can be calculated as . The next triangle is If we want the area of the green triangle it is but we have already calculated the red triangle. So the area we want in addition is or if we focus on the trapezoid . In general, the Gini coefficient may be calculated from the following formula for area B : where x i and y i are the two cumulative relative frequencies on the X and Y axis. x = y = 0 and x k = y k = 100 (or 1). Alternatively, the Gini coefficient can be expressed as In case where x k = y k = 100, the area . Hence...
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## This note was uploaded on 02/26/2011 for the course BUSINESS Bus061 taught by Professor Hidi during the Spring '11 term at West Valley.

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How to calculate Gini coefficient - area for the triangles...

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