A small startup has five employees with annual salaries of $30,000, $40,000, $50,000, $60,000 and $70,000. Use the Gini Index to measure the income inequality among the employees.
Answer
Step 5: Finally, the Gini Index is given by \[ G = \frac{A}{A+B} \] or equivalently \[ G = 1 - \frac{2B}{A+B} \].
Step 1 ：Step 1: First, we need to calculate the average income. It is given by the formula \[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \], where \(x_i\) are the incomes and \(n\) is the number of employees.
Step 2 ：Step 2: Next, we calculate the cumulative incomes and cumulative percentages of both incomes and population.
Step 3 ：Step 3: Then, we calculate the area A between the line of perfect equality (a diagonal) and the Lorenz curve (the actual distribution).
Step 4 ：Step 4: We also calculate the area B under the Lorenz curve.
Step 5 ：Step 5: Finally, the Gini Index is given by \[ G = \frac{A}{A+B} \] or equivalently \[ G = 1 - \frac{2B}{A+B} \].
