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.

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Accepted Answer

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} ].

Answer

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} ].

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.

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Popular Problems

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

Popular Problems

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.