Gini Coefficient: Step by Step Calculation from Lorenz Curve

From Lorenz curve we can only visualize the distribution or the inequality in the distribution. No numeric expression is got from the curve about the distribution.

Thus Gini in 1912 devised a method of determining the coefficient of inequalities from the Lorenz carve. It is actually the ratio between the area within the diagonal line (A) and the line of actual distribution and the area under the diagonal line (A+B). 

Fig.1: Lorenz Curve

The equation is, 

The value of i ranges between 0 and 1 (0 and 100 if expressed in percentage.)

0≤Gi ≤1

0 means no inequality or perfect equality which means everyone has the same income or wealth and 1 means perfect inequality which means one person have all the income. 

Gini coefficient can be computed from the table of Lorenz curve. 

Example-1: Calculate the Gini Coefficient from the Lorenz Curve Data Table

Equation: 

Table: Calculation of Gini Coefficient
Cumulative % Tot Pop (Xi)	Cumulative % Urban Pop (Yi)	(Xi*Yi+1)	(Xi+1*Yi)
7.6	0.5	19.0	6.1
12.1	2.5	78.8	45.4
18.2	6.5	290.6	187.8
28.9	16.0	621.3	558.9
35.0	21.5	1275.1	1043.2
48.5	36.5	4466.5	3479.0
95.4	92.0	9536.6	9204.9
100.0	100.0	16287.9	14525.3
		Gi=	0.176

Steps:

1. Multiply the X values with Next Y values and put on the third column. 

2. Similarly multiply the Y values with next X values and put on the fourth column.

3. Make summation of the 3rd and 4th columns.

4. Divide the difference of the 3rd and 4th column with 1/10000 to get the Gini Score.

Interpretation of Gini coefficient value: Gini value for this data is 0.176 which is close to zero and far away from one. Thus the disparity or inequality in the distribution of urban population is minimum.