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Lorenz Curve is a probability distribution curve that is used for measuring the variability of a statistical series. This curve was developed by Max Lorenz in 1905. The curve is very popular in Economics for measuring the distribution of wealth and income in society.
Lorenz Curve measures the standard deviation of an actual distribution from the line of equal distribution. Put it simply, it measures the deviation of a present distribution from an imaginary or hypothetical distribution.
The difference between the actual distribution and the hypothetical distribution or the extent of deviation is known as Lorenz Coefficient. The greater the difference or deviation of the Lorenz Coefficient, the greater is the inequality or variability in the distribution. In the same way, if the difference is lower in comparison then it can be said that the inequality or variability in the distribution is lower.
Constructing a Lorenz Curve
Here are the steps for the construction of Lorenz Curve
- A discrete series is taken and the values are converted into cumulative frequency series. Assume that the cumulative sum of items is 100 and the items in the cumulative sum are converted into percentages of the sum of frequencies.
- On X-axis, these cumulative frequencies are plotted and on Y-axis the cumulative items are plotted.
- Take a graph sheet and mark both X and Y axes taking values from 0-100.
- Now, draw a line diagonally from X (0,0) to Y (100, 100). This is the equal distribution line or the Line of equal distribution.
- Now, in the graph sheet, mark the cumulative frequency values and compare them with the Line of equal distribution.
- You can take the highest point of difference between the line of equal distribution to the line of actual distribution.
- This line of Actual Distribution is called the Lorenz Curve, where the greater the difference, the larger the gap, and vice versa.
Application of Lorenz Curve
Lorenz Curve is applied in a number of studies or subjects. One of the subjects where the Lorenz Curve has been applied more is in economics. In economics, Lorenz Curve is used for studying income distribution, wealth distribution, wage distribution, profit distribution, production distribution, population distribution, etc.
Image Credit: Wikipedia
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