The formula to calculate the Gini Index (GI) is:
\[ GI = 1 - 2 \left(1 - \frac{\sum_{i=1}^{n} (n + 1 - i) y_i}{n \sum_{i=1}^{n} y_i}\right) \]
Where:
The Gini Index is a measure of statistical dispersion intended to represent the income inequality or wealth inequality within a nation or a social group. It is a number between 0 and 1, where 0 corresponds to perfect equality (everyone has the same income) and 1 corresponds to perfect inequality (one person has all the income, and everyone else has none).
Let's assume the following data points: 10, 20, 30, 40, 50
Using the formula to calculate the Gini Index:
\[ GI = 1 - 2 \left(1 - \frac{350}{5 \cdot 150}\right) = 1 - 2 \left(1 - \frac{350}{750}\right) = 1 - 2 \left(1 - 0.4667\right) = 1 - 2 \cdot 0.5333 = 1 - 1.0667 = -0.0667 \]
The Gini Index is approximately -0.0667.