### Statistics of Income: A Math, Technology, Economics, Sociology Thematic Lesson

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.

Written: 2003

Modified: January 2010

# Statistics and Economic Power

## Basic Spread Sheet Project

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.gov/taxstats/indtaxstats/article/0,,id=96981,00.html (If this link changes search the IRS site for "SOI")
3. From this page, download into your folder the latest SOI. The file will probably have a name like 07in11.xls. This is Excel format.

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

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

A: Starting

1. Take time to examine how the files are set up. What units are the columns reporting? Do the money columns report total for the group, or average for the group?
2. Determine which columns you will need to use to determine median, average, and percentile. Notice that median and average will not depend on the same column.
3. Once you have determined which columns contain the pertinent information and how it is reported, use spread sheet formulas to calculate the median and the average.
4. How much money does the median earner make? How far from the median is the average income? Why are they so far apart?

B: Finding Percentiles

1. Check the chart again. Does this chart report percentiles? If not create a column to calculate percentiles for each group (row).
2. Can you find the 50, 25, and 75 percentiles? Can you find numbers close?
3. Use interpolation formulas to get a more accurate estimate of the 25, 50 75 percentile?
4. What annual income do you consider rich? What annual income do you consider poor? Determine what percentile correlates to those incomes.

Section C: Graphing the Data

1. Create a graph plotting percentile against income? What part of the graph is hard to read? What part is easy to read?
2. Convert the income scale to logarithmic. Now what part of the scale is hard to read?
3. Do you notice any distinct bends in the graph? If so, where do they occur?

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. How did the size of the group in poverty compare to the size of the rich group? How did the total income of the group in poverty compare to the total income of the rich group?
3. For the two graphs you made, why is the second graph better for viewing low incomes, and the first only good for large incomes?
4. What is meant by "adjusted gross income?"  Could this definition affect the quality of the data?

Related Pages at this site:

Extensions:

1. Look at the graphs showing changes over the decades. 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 outliers, natural groupings, ... Which method do you think has the most meaning for this data? 