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Lorenz curve? |
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Answer» How u sre inserting all the graph and tables on this app Lorenz Curve is a curve which measures the distribution of wealth and income. Now it is also used for the study of the distribution of profits, wages etc.Lorenz CurveThe 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\xa0Example 16\xa0\xa0\xa0\xa0\xa0Construction of the Lorenz Curve\xa0Following steps are required.\tCalculate class mid-points and find cumulative totals as in Col. 3 in the example 16, given above.\tCalculate cumulative frequencies as in Col. 6.\tExpress 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.\tNow, 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\'.\tDraw 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.\tPlot the cumulative percentages of the variable with corresponding cumulative percentages of frequency. Join these points to get the curve OAC.Studying the Lorenz CurveOC 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. |
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