A sociologist studying the distribution of income in an industrial society compiles the data displayed in the accompanying table, where L(x) denotes the fraction of the society’s total wealth earned by the lowest-paid 100x% of the wage-earners in the society. Use this information together with the trapezoidal rule to estimate the Gini index (GI) for this society; that is,

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0 0.125 L(x) 0 0.0063 X GI= 2 [x L(x)] dx = 2√ Lx² 0.25 0.0631 0.375 0.5 0.1418 0.2305 0.625 0.3342 0.75 0.875 1 0.4713 0.6758 1