In the summer of 2008, the Washington Post ran a story on the performance of Montgomery County in the 2008 state math assessment tests. The story said that of 24 counties in Maryland, Montgomery County was 11th in terms of its passing rate. However, the reporter was unable to draw a conclusion about whether this was good or bad.
Your job is to help the reporter sift through the data. I have downloaded the data for all 24 Maryland counties and placed into a spreadsheet, which you can download.
The columns of the spreadsheet are as follows:
County: the name of the county
total students: the total number of students who took the math assessment test
FARMS: of the students who took the math assessment test, the number on Free and Reduced Meals (an indicator of disadvantaged backgrounds)
basic: the number of students who scored "basic" (not passing) on the test
prof: the number of students who scored proficient
adv: the number of students who scored advanced
pct NF: the proportion of students who were not FARMS, that is who are not disadvantaged
pct pass: the proportion of students who passed, meaning that they scored proficient or advanced
spending: average spending per student in the 2005-2006 school year
For the the last three columns, the spreadsheet includes the mean and the standard deviation at the bottom of the columns.
The focus is on the data in the last three columns. Montgomery County indeed was 11th in its passing rate. It was 1st in its spending rate. However, the story indicated that Montgomery County does not have as high a rate of non-disadvantaged students as it used to. Try to use the data to sort all this out.
Things you might try for each of the three key items of proportion of non-FARMS, proportion that pass, and spending rate:
Set up three new columns and rank the counties from 1 to 24 in terms of proportion of non-FARMS, proportion of students who passed, and spending per student. You can do this by hand, or, if you use Excel, there is a function that will do it for you.
Next, find the median, first quartile, third quartile, and the range for each. The median in a list of 24 is in betwen the 12th and the 13th in the ranking. The first quartile is between the 6th and 7th. The third quartile is between the 17th and 18th.
Next, list the top 5 counties in each category. List the bottom 5 counties in each category. Look for patterns and for exceptions to patterns.
Next, try scatterplots. Try a plot with spending on the horizontal axis and pass rate on the vertical axis. Try a plot with non-FARMS on the horizontal axis and pass rate on the vertical axis. Do the plots show a relationship? Are there important exceptions to the relationship?
Come to some sort of conclusion. How well is Montgomery County doing, relative to other counties, in math education, given its population? Justify your conclusion.