Gini Index Calculator

Calculate the Gini coefficient (Gini index) from a list of incomes or other values, or Gini impurity from class counts for a decision tree node.

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Gini Index Formula

The following formula is used to calculate the Gini Index (Gini coefficient) from non-negative data sorted in ascending order.

GI = 1 + 1/n – (2 / (n * Σ_(i=1)⁽ⁿ⁾ y_i)) * Σ_(i=1)⁽ⁿ⁾ (n + 1 – i) * y_i

Variables:

• GI is the Gini Index
• n is the number of data points
• y_i is the i-th data point in ascending order

To calculate the Gini Index, first sort the data points in ascending order. Then compute the sum of all data points, Σ_(i=1)⁽ⁿ⁾ y_i. Next, compute the weighted sum Σ_(i=1)⁽ⁿ⁾ (n + 1 – i) * y_i. Finally, substitute these into GI = 1 + 1/n – (2 / (n * Σ y_i)) * Σ (n + 1 – i) * y_i. With a positive total, this uncorrected empirical formula ranges from 0 (equal values) to 1 − 1/n for n observations. An all-zero total is undefined; no sample-size correction is applied.

Weighted Gini of a Decision-Tree Split

Choose Weighted Gini of a decision-tree split to evaluate a proposed split. Enter one child node per line, with the count for each class in the same column on every line. Use zero for a class absent from a child. Each child must contain at least one item. The calculator displays each child’s impurity and weights it by that child’s share of the total item count.

For child j, n_j = Σ_k c_jk, p_jk = c_jk/n_j, and G_j = 1 − Σ_k p_jk². With N = Σ_j n_j, weighted Gini = Σ_j (n_j/N) × G_j. The parent counts are the column sums of all children. Gini gain = parent impurity − weighted Gini; a larger gain means a greater reduction in class mixing for this split. This is a classification impurity measure, separate from the income-inequality coefficient. The tool evaluates supplied child nodes; it does not find a split threshold or accept survey weights.

How to Calculate Gini Index?

The following steps outline how to calculate the Gini Index.

1. First, determine the number of data points (n).
2. Next, arrange the data points in ascending order.
3. Next, calculate the sum of all the data points (Σ_(i=1)⁽ⁿ⁾ y_i).
4. Next, calculate the sum of (n + 1 – i) * y_i for each data point.
5. Next, calculate GI = 1 + 1/n – (2 / (n * Σ_(i=1)⁽ⁿ⁾ y_i)) * Σ_(i=1)⁽ⁿ⁾ (n + 1 – i) * y_i.
6. Finally, report the Gini Index (GI).
7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Number of data points (n) = 5

Data points (y_i) in ascending order: 1, 2, 3, 4, 5. Their total is 15 and the Gini coefficient is 0.266667 (Gini index 26.6667 on a 0–100 scale).