GATE 2022 AR — Architecture – Question 49
The Lorenz graph shows cumulative population/income points (0, 0), (30, 18), (70, 45), (100, 100), in percent. Find the Gini coefficient to three decimal places.
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Correct answer: 0.240 to 0.270
Explanation
Convert to fractions and add trapezoidal areas under the Lorenz curve:0.3×0.18/2=0.027; 0.4×(0.18+0.45)/2=0.126; 0.3×(0.45+1)/2=0.2175. Total area is 0.3705. Gini=1−2×0.3705=0.259. It is dimensionless; do not report 25.9 as the coefficient.