The Lorenz Curve: In this problem, we'll work step-by-step through constructing values of a Lorenz functionfrom a set of raw data. This will help you to understand the meaning of the Lorenz curve,(a) A small village has a population of 10 people. The yearly incomes, in thousands of CAD per year, for eachof the 10 residents is listed below.78, 35, 55, 100, 46, 80, 35, 25, 68, 78Rearrange these incomes in increasing order, from smallest to largest.(b) What is the total sum of the income made by all people in this town each year?(c) What fraction of the total income is made by top 20% of earners? Please express your answer as a decimalvalue between 0 and 1.(d) What fraction of the total income is made by bottom 20% of earners? Please express your answer as adecimal value between 0 and 1. (Hint: Even if there is a tie for the second-lowest earner, you should onlycount two of the 10 people as the lowest-earning 20%.)(e) Please continue by filling in the chart below. All mumbers in the second row should be in CAD, while allnumbers in the third row should be decimal values between 0 and 1. You may round numbers in the thirdrow to the nearest hundredth.Lowest-earning fraction rTotal income (K CAD) made bylowest-earning fraction rFraction of income made bylowest-earning fraction r(f) The Lorenz function L(x) represents the fraction of the population's total income made by the lowest-earning fraction r of people in the population. In this case, the numbers that you wrote in the third rowof the above table represent values of L(1). Please plot these points on the grid below. (When graphed,these become points on the Lorenz curve, which is the graph of the Lorenz function.)0.00.20.40.60.81.01.0y = L(x)0.80.60.40.20.2 0.4 0.6 0.8 1.0

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The Lorenz Curve: In this problem, we'll work step-by-step through constructing values of a Lorenz function from a set of raw data. This will help you to understand the meaning of the Lorenz curve, (a) A small village has a population of 10 people. The yearly incomes, in thousands of CAD per year, for each of the 10 residents is listed below. 78, 35, 55, 100, 46, 80, 35, 25, 68, 78 Rearrange these incomes in increasing order, from smallest to largest. (b) What is the total sum of the income made by all people in this town each year? (c) What fraction of the total income is made by top 20% of earners? Please express your answer as a decimal value between 0 and 1.

The Lorenz Curve: In this problem, we'll work step-by-step through constructing values of a Lorenz function from a set of raw data. This will help you to understand the meaning of the Lorenz curve, (a) A small village has a population of 10 people. The yearly incomes, in thousands of CAD per year, for each of the 10 residents is listed below. 78, 35, 55, 100, 46, 80, 35, 25, 68, 78 Rearrange these incomes in increasing order, from smallest to largest. (b) What is the total sum of the income made by all people in this town each year? (c) What fraction of the total income is made by top 20% of earners? Please express your answer as a decimal value between 0 and 1.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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