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Grade 9-12

Distribution of Income

Updated: May 31 2017,
Author: Beth RempeGrant Black
Open Lesson

Assessment Activity

  1. Who would likely earn the most income?

    1. Bob, who did not graduate from high school and works part-time at a fast-food restaurant
    2. Jo, who just graduated from high school and started working at her first full-time job two months ago
    3. Nick, who has a bachelor’s degree and is working on a master’s degree part-time while working as an entry-level manager at a small company
    4. [Sarah, who just started working at a law firm after graduating from law school]
  2. What would likely be the effect of a government policy that increased income equality by taxing the fifth quintile to transfer income to the first quintile?

    1. Incomes in the first and fifth quintiles are less than before the policy.
    2. Incomes in the first and fifth quintiles are more than before the policy.
    3. Incomes in the first quintile are less and incomes in the fifth quintile are more than before the policy.
    4. [Incomes in the first quintile are more and incomes in the fifth quintile are less than before the policy.]
  3. Calculate the mean income for the following four people.










  1. $47,500
  2. [$50,000]
  3. $52,500
  4. $200,000

Short Answer:

The Lorenz curves for two different income distributions are shown in the following graphs:

Graph 1

Graph 2

  1. Analyzing the shape of the Lorenz curve, explain which distribution you think exhibits less income inequality. [Graph 2 exhibits less income inequality than graph 1 because its Lorenz curve is less convex or “bowed.”]
  2. Using data from each graph, calculate the Gini coefficient for each income distribution. [Graph 1 curve has a Gini coefficient of 0.4 and graph 2 curve has a Gini coefficient of 0.2.]
  3. What does the Gini coefficients from each graph, tell you about the distribution of income inequality? [Graph 1 Gini coefficient of 0.4 represents more income inequality. The most unequal income would be represented by a Gini coefficient equal to 1. Graph 2 Gini coefficient of 0.2 represents less income inequality. The most equal income distribution would be represented by a Gini coefficient equal to 0.]
  4. Create a government policy to redistribute income that could explain the difference between the two income distributions shown in graphs 1 and 2 and briefly summarize your policy. [Answers will vary, but students may say that their policy redistributes income by transferring income through government taxation and tax credits, spending, or assistance programs to target particular income groups with the goal of transferring income from higher-income groups to lower-income groups. Alternative programs might include increased job training and education.]


The personal distribution of income is the way analysts organize income by categories such as households, families, or even individuals. The level of income usually depends on the productivity of workers and other factors that affect the structure of the economy, such as government policies, technology, or discrimination. Differences in productivity across individuals can contribute to income inequality.

Mathematics and statistics provide tools to analyze the distribution of income and income inequality. The mean and median provide measures of central tendency for the distribution of income. The Lorenz curve graphically represents the distribution of income across a population. While the mean and median condense information about the income distribution to single summary statistics, the Lorenz curve provides more perspective about the distribution of income. Comparisons between different income distributions can be made by analyzing differences in statistics, such as the mean and median, and the Lorenz curve. For example, comparing the mean and median income of people in an economy is common. Using median income can avoid some of the pitfalls of averages.

Changes in productivity and structural factors like government policies can alter the distribution of income. Government often uses policies to redistribute income to reduce income inequality. Government taxation is one means of redistributing income. Progressive income taxes, for example, redistribute income in favor of lower income households.  Redistribution of income can also occur through a transfer of income, spending and assistance programs, and programs designed to provide training to workers. A goal of reducing income inequality might involve transferring money from higher-income groups to lower-income groups. While some redistribution policies may increase income for some groups, some of these policies, at the same time, may distort economic incentives by weakening the relationship between productivity and income. Other policies could have different effects.

Mathematics and statistics also provide ways to effectively analyze the level of income equality and changes in the distribution of income. Changes in the distribution of income can be reflected in changes in measures of central tendency, such as the mean and median, as well as changes in a Lorenz curve. Income inequality can be measured by comparing measures of central tendency and by calculating a Gini coefficient based on a Lorenz curve. The degree of income inequality is quantified by a Gini coefficient, and changes in the value of the Gini coefficient indicate changes in income inequality.