# What is Gini index?

Gini index is the most commonly used measure of inequality. Also referred as Gini ratio or Gini coefficient.

Gini index for binary variables is calculated in the example below.

 Student inHostel Target Class Yes True Yes Yes True Yes Yes False No False False Yes False True No False True No False False No True False Yes False True No

Now we will calculate Gini index of student and inHostel.

Step 1:

Gini(X) = 1 [(4/9)2 + (5/9)2] = 40/81

Step 2:

Gini(Student = False) = 1 [(1/5)2 + (4/5)2] = 8/25

Gini(Student = True) = 1 [(3/4)2 + (1/4)2] = 3/8

GiniGain(Student) = Gini(X) [4/9· Gini(Student = True) + 5/9· Gini(Student = False)] = 0.149

Step 3:

Gini(inHostel = False) = 1 [(2/4)2 + (2/4)2] = 1/2

Gini(inHostel = True) = 1 [(2/5)2 + (3/5)2] = 12/25

GiniGain(inHostel) = Gini(X[5/9· Gini(inHostel = True) + 4/9· Gini(inHostel = False)] = 0.005

Results

Best split point is Student because it has high gini gain.

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