Weighted Gini

A single split creates two child groups—a left group and a right group. Weighted Gini combines their impurity scores into one number the tree can compare.

After a split, each child may have a different Gini score and a different number of samples. A tiny but very pure group should not outweigh a large mixed group.

Weighted Gini averages the left and right Gini values, giving more weight to the side with more samples. The tree uses this score to judge whether a split is good.

$$\text{Weighted Gini} = \frac{n_{\text{left}}}{n} \cdot \text{Gini}(\text{left}) + \frac{n_{\text{right}}}{n} \cdot \text{Gini}(\text{right})$$

Here $n$ is the total number of samples in the parent node, and $n_{\text{left}}$ and $n_{\text{right}}$ are the sizes of each child.

Split rules:

• Left: samples where $x \leq t$
• Right: samples where $x > t$

On our 8-sample practice dataset, splitting Feature 0 at threshold $t = 2.5$ gives:

$$\text{Weighted Gini} = \frac{4}{8}(0.375) + \frac{4}{8}(0) = 0.1875$$

Averaging Gini values without weighting by sample count. Two children of unequal size need the $\frac{n_{\text{left}}}{n}$ and $\frac{n_{\text{right}}}{n}$ factors—otherwise a small group can skew the result.

Weighted Gini is how a decision tree scores one candidate split. Lower weighted Gini means the split produced cleaner child groups overall.

Use the Weighted Gini Calculator below to adjust left and right class counts and see the weighted score change.