Given below are the monthly incomes of employees of a company. Draw a Lorenz Curve with it. Also write down the steps required for drawing a Lorenz Curve.
|
Incomes |
Number of Employees |
|
0–5,000 |
5 |
|
5,000–10,000 |
10 |
|
10,000–20,000 |
18 |
|
20,000–40,000 |
10 |
|
40,000–50,000 |
7 |
|
Income limits |
Midpoints |
Cumulative mid-points |
Cumulative midpoints as percentages |
No. of employees frequencies |
Cumulative frequencies |
Cumulative frequencies as pecentages |
|
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
|
0-5000 |
2500 |
2500 |
2.5 |
5 |
5 |
10 |
|
5000-10000 |
7500 |
10000 |
10.0 |
10 |
15 |
30 |
|
10000-20000 |
15000 |
25000 |
25.0 |
18 |
33 |
66 |
|
20000-40000 |
30000 |
55000 |
55.0 |
10 |
43 |
86 |
|
40000-50000 |
45000 |
100000 |
100.0 |
7 |
50 |
100 |
Steps required for the construction of a Lorenz Curve : Following steps are required for the construction of a Lorenz Curve :
1. Calculate class mid-points and find cumulative totals as in Col. 3 in the questions, given above.
2. Calculate cumulative frequencies as in Col. 6.
3. Express the grand totals of Col. 3 and 6 as 100, and convert the cumulative totals in these columns into percentages, as in Col.4 and 7.
4. Now, on the graph paper, take the cumulative percentages of the variable (incomes) on Y axis and cumulative, percentages of frequencies (number of employees) on X-axis, as in figure. Thus each axis will have values from ‘0’ to ‘100’.
5. Draw a line joining Co-ordinate (0,0) with (100,100). This is called the line of equal distribution shown as line ‘OC’ in figure.
6. Plot the cumulative percentages of the variable with corresponding cumulative percentages of frequency. Join these points to get the curve OAC.
