Question

Given the following income data from a representative sample of a population in a certain year, what is its Gini index?

Person	Income	Person	Income	Person	Income
1	30	6	400	11	1700
2	70	7	550	12	2000
3	140	8	1100	13	3000
4	210	9	1200	14	5000
5	300	10	1450	15	8000

	A.	0.34
	B.	0.44
	C.	0.57
	D.	0.60
	E.	0.76

Answer 1

Person	Income	% of population	% of income	cummulative % of income	area under the Lorenz curve (i.e., B)
1	30	0.067	0.001	0.001
2	70	0.133	0.003	0.004	0.00016
3	140	0.200	0.006	0.009	0.00044
4	210	0.267	0.008	0.018	0.000906
5	300	0.333	0.012	0.030	0.001585
6	400	0.400	0.016	0.046	0.002518
7	550	0.467	0.022	0.067	0.003783
8	1100	0.533	0.044	0.111	0.005981
9	1200	0.600	0.048	0.159	0.009045
10	1450	0.667	0.058	0.217	0.012575
11	1700	0.733	0.068	0.284	0.01677
12	2000	0.800	0.080	0.364	0.021699
13	3000	0.867	0.119	0.483	0.028359
14	5000	0.933	0.199	0.682	0.039015
15	8000	1.000	0.318	1.000	0.056331
	Sum= 25150				Sum = 0.199167

Area of A = 0.5 - Area of B

Area of A = 0.5 - 0.199167

Area of A = 0.30

Gini Coefiicient = (Area of A / 0.5)

Gini Coefficient = 0.60

Answer: Option (D).