Activity 2.2
State Governors' Salaries and Per Capita Income: More on Scatterplots
10 points
Due at the beginning of class, Wednesday, February 4, 2009
In this activity you will use scatterplots to investigate the relationship between the governor's salary and the average per capita income in the state. You will also analyze differences between scatterplots and other types of graphs.
The following table gives the average per capita income and governor's salary in 2007 for each state in a group of nine northeastern states.
| State | Per Capita Income 2007 | Governor's Salary 2007 |
| Connecticut | 54,984 |
150,000 |
| Maine | 33,962 |
70,000 |
| Massachusetts | 49,142 |
140,535 |
| New Hampshire | 41,444 |
108,990 |
| New Jersey | 49,238 |
175,000 |
| New York | 46,664 |
179,000 |
| Pennsylvania | 38,740 |
164,396 |
| Rhode Island | 39,712 |
105,194 |
| Vermont | 37,446 |
150,087 |
1. Explain how you would use a bar graph to represent and interpret one or more aspects of the data. Which aspects of the data would the bar graph represent?
2. Would a histogram help interpret the data, or an aspect of the data? Explain.
3. Which type of graph would help you answer the question: Is there any relationship between per capita income in a state and the governor's salary?
4. On a separate sheet of paper (which you should turn
in), create a scatterplot using the two quantitative variables,
"per capita income" and "governor's salary."
5. Which variable did you use on the x-axis? Why?
6. Which variable did you use on the y-axis? Why?
7. Explain what your graph shows about the relationship of the two variables.
8. To analyze this relationship further you will create a scatterplot using data on all 50 states. To do so, you will first create a two-column table that records the governor's salary and the average per capita income for each state. The files containing the data are EA2.2.1 Per Capita Income.xls and EA2.2.2 Governors Salaries.xls.
9. Create a scatterplot of this data set. You should change the scale of the horizontal (or x) and vertical (or y) axes so the data are easier to read. (To change the scale on an axis, point to the axis and either double-click or right-click and select Format axis. Then on the Scale tab, enter the appropriate minimum and maximum values for the axis.) What is a reasonable minimum value of x to use? What about y?
10. Are there any trends or patterns to this data? Explain.
11. Are there any data points that appear to be "away from" the rest of the data? If so, which (ones) and what makes them stand out?
Summary
In this activity, you considered the differences among a bar graph, a histogram,
and a scatterplot and the information conveyed. You learned to copy and paste
in Excel. You looked at trends in a sample compared to trends in a full data
set and looked for unusual observations. You also investigated trends over time
and relationships between variables.