These examples use bubble charts to show the relationship between educational performance, expenditures, and student-teacher ratios by state. The size of each bubble shows the population of each state.
Student-teacher ratios: Statemaster.com.
Math and Reading Assessments (Grade 8, Y2007): US Dept of Education – National Center for Educational Research
Median Spending per Student (FY2007): US Dept of Education – National Center for Educational Research
Cost of Living (4Q2008): Top50States.com: Cost of Living by State
This graph shows that math and reading scores by state are highly correlated.
Move your mouse over a data point to see details about the data point. Also, you can zoom into a part of the graph as follows:
- Press the left mouse button to mark the lowest X value of interest in the graph. A vertical red line will appear.
- Move the mouse to the highest X value of interest.
- Press the right mouse button and select Zoom Middle from the pop-up context menu.
When zooming, you can use the scroll bar below the graph to change the range of values that are displayed.
The graphs above show the relationship between Math and Reading scores vs. spending. Color encodes the geographic region of each state. These graphs show that Northeastern states (in blue) tended to spend more money per student and achieved higher scores. However, high scores were also achieved by some states with median spending levels. Examples include Minnesota and Kansas, and North Dakota in Math, and Montana and South Dakota in Reading.
The graphs above show scores vs. median per-student spending that has been divided by the relative cost of living in each state. These graphs show a somewhat stronger correlation compared to the graphs that used unnormalized spending per student. The costs of living in New York, New Jersey, Massachusetts, and California are more than 20% higher than the national average, so normalizing the median per-student spending by the cost of living results in a relatively lower value. When cost of living is factored, California spends less per student than any other state. Most of the states that spent $10,500 or more per student (normalized) achieved reading scores higher than 262. To see this more easily, press the left mouse button at x=10500, y=262.
The graphs above show the relationship between Math and Reading scores and student-teacher ratios. Color encodes the geographic region of each state. Western states, shown in green, tend to have higher class sizes. Northeastern states, shown in blue, tend to have smaller class sizes. Except for Minnesota and Colorado, nearly all states that achieve an average reading score of 266 or better have an average class size smaller than 15.4. However, there are also many states with small class sizes that performed less well in Reading.
The graphs above show the relationship between Math and Reading scores and a derived statistic that is computed by dividing each state’s normalized per-student spending by its average student-teacher ratio. This statistic is higher for states with higher spending and lower student-teacher ratios and represents the combined effect of spending and class size. Except for Alaska and Rhode Island, all states with derived statistics greater than 850 achieved Math scores greater than 280 and Reading scores greater than 263.