# Lorenz Curve

The measures of dispersion discussed so far give a numerical value of dispersion. A graphical measure called Lorenz Curve is available for estimating dispersion. You may have heard of statements like 'top 10% of the people of a country earn 50% of the national income while top 20% account for 80%'. An idea about income disparities is given by such figures. Lorenz Curve uses the information expressed in a cumulative manner to indicate the degree of variability. It is especially useful in comparing the variability of two or more distributions. Given below are the monthly incomes of employees of a company.

TABLE 6.4

Example 16

Construction of the Lorenz Curve

Following steps are required.

1. Calculate class mid-points and find cumulative totals as in Col. 3 in the example 16, 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 6.1. 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 6.1.
6. Plot the cumulative percentages of the variable with corresponding cumulative percentages of frequency. Join these points to get the curve OAC.

# Studying the Lorenz Curve

OC is called the line of equal distribution, since it would imply a situation like, top 20% people earn 20% of total income and top 60% earn 60% of the total income. The farther the curve OAC from this line, the greater is the variability present in the distribution. If there are two or more curves, the one which is the farthest from line OC has the highest dispersion.

Courtesy NCERT Text book