# What is the interval of Gini Index?

Suppose we have 2 classes.

C1: 0
C2: 6


The Gini index is: $1−(0÷6)^2−(6÷6)^2 = 0$

C1: 3
C2: 3


The Gini Index is: $1−(3÷6)^2−(3÷6)^2 = 0.5$

So am I right, when I say, the Gini Index lays in the Interval of $0$ and $0.5$?
I can't think of any other examples, where it gets higher than $0.5$.

Edit:
Except, when there are more than 2 classes. It that even possible?

• It's in the interval [0,1] unless you allow for negative income/wealth/etc. en.wikipedia.org/wiki/Gini_coefficient – C8H10N4O2 Feb 8 '16 at 19:07
• In finite populations or samples, the Gini index has an upper bound of 1-1/n, page 869 in Measures of Inequality, American Sociological Review (Allison, 1978). PDF. – Andy W Feb 9 '16 at 13:44