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Question: Lorenz curve y = f (x) is used to represent a wealth distribution in a nation. The entire population is plotted along the x-axis from poorest to richest, and the height of the curve on the y-axis shows the percentage of total income received by the proportion of the population given on the x-axis. Graph of function y = x, called the line of perfect equality, represents the population where everyone has the same income. The area between the graphs of the two functions for 0 ≤ x ≤ 100 shows the country's income inequality.
The table below gives the percentage of income for selected percentages of people in a country.
x
10
20
30
40
50
60
70
80
90
y
3.32
6.41
8.96
12.39
19.32
28.11
38.65
55.13
78.29
Use Excel to fit a quadratic curve to the given data. Plot the data along with the obtained curve above and the line y = x. Using the obtained curve, approximate the income inequality for the given country.
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