Statistics of Income Lesson for High School

Motivation: All too often students learn new mathematical ideas without having the resources available to make those ideas meaningful. This lab is designed to be used thematically between the social studies, technology, and math classes. This lab gives students a chance to compare what they believe about wealth to what the statistics imply.

Objectives: Students will develop an application for statistical concepts by applying statistics to common values based discussions in economics. Students will use technology to analyze data. Students will recognize that math does not always result in one single answer, but instead becomes the basis for discussion.

Background: This lesson was used in an inner-city high school. The lesson was coordinated between the math and technology classes so that students would finish their graphs and discussions in the computer lab in time to be discussed in the math class.

It is suggested that the social studies and math teacher modify the questions at the end, and the procedures to support those questions to the skill level of the classes. Otherwise, cut and paste starting here:

# Statistics and Economic Power

In this project, you will organize the IRS statistics of Income and create graphs to focus on the questions: Who has great economic power?  Who does do not? How much economic power do those at the top really have?

To do all this, you will use the standard concepts of statistics such as, median, mean, percentile and variance.  You will also use the standard tools of statistics including charts, graphs, and spread sheets.

### Part 1: Acquiring the data:

1. Create a folder called IRS Data on your tech lab network disk.
2. Go to the IRS page:  http://www.irs.ustreas.gov/prod/tax_stats/soi/ind_agi.html
4. Go to your folder and click on this file.  This will create 4 files.

### Part 2: Median, Percentile, & Quartile:

In this section you will calculate and interpret median, percentile and quartile.

A: Setting up the file:

1. Create an Excel file called Percentile
2. Put your name in cell A1
3. Open the IRS file INDT1
4. Copy and paste the first 3 column sections from INDT1 (cells A6 to C31) into your file
5. Raise the columns so that you can see the numbers. Remember the symbol: ######## means that a number is too large to be seen in a column this narrow.

B: Organizing the data:

Examine the 3 columns you have copied.  The first column is a text field reporting ranges of income.  The second column is a number field reporting count (frequency) of taxpayers within this range.  The third column is number of thousands of dollars earned within this range.  For our calculations this organization is not very useful. We will need to calculate some more information.

1. To calculate percentile will take 2 columns. First, in column D corresponding to no income (cell D15 if you copied to the same cells copy over the number of return with no income ( use: =B15)
2. From here we want to create a column adding all the lower numbers. To do this, in the next cell (D16) add the cell from row B with the cell above (use: =B16+D15)
3. Above the numbers in column D put the label "Integral"
4. Copy and paste this formula into the cells below, until you reach the million dollar range. (D29)
5. Now you may calculate percentiles. In each cell in Column E calculate percentile by dividing the value in D by the total returns (B14) and multiplying by 100.   E.g.: cell E15 gets = D15/B14*100
6. Format column E to have 1 digits after the decimal place.
7. Check that the list goes from 0 to 100.
8. Above the numbers in column E put the label "Percentiles"
9. Now in column F we will determine the average income for each range.  This will be done by dividing column C by column B and multiplying in the 1000 (e.g.:  =C15/B15*1000 )
10. Label column F as "average income by range"

Section C: Graphing the Data

Here we will create graphs to represent the data.

1. Highlight the numbers in columns E & F
2. Click on the graph symbol
3. Pick X-Y scatter and pick the first option with curves.
4. On the titles page, label the x-axis as: "Percentile of Wage Earner"  and label the y-axis as "income."
5. Create a second graph, using all but the last 4 values (highlight E15 to F24)

Section D:  Using Data and Graphs to Reason about Economic Power

Use the charts and graphs you created to answer the following questions.

1. What is meant by the negative number for income correlating to the range: "No adjusted gross income"?
2. Estimate the Income of the Median (50th percentile), 1rst quartile, and 3rd quartile.
3. What range of incomes do you think correspond to economically poor? What percent of the population is in this range?
4. What range of incomes do you think corresponds to economically "rich"?  What percent of the population is in this range?
5. For the two graphs you made, why is the second graph better for viewing low incomes, and the first only good for large incomes?
6. What is meant by "adjusted gross income?"  Could this definition affect the quality of the data?

Extensions:

1. Look at the graphs comparing 1980 to 1990 at: http://webspace.webring.com/people/qg/gordonite32/musings/economy/Economy.html Do you agree with the implications stated by the author of this page. Pick two years for comparison and create the same graphs. Discuss the change in economic climates differed for the rich, the middle class, and the poor.
2. Compare different methods of determining range or variance for this data, e.g.: the gaussian formula, throwing out the outlyers, natural groupings, ... Which method do you think has the most meaning for this data?