Activity 1.3

SATs and the Super Bowl: Creating and Interpreting Histograms

10 points

Due at the beginning of class, Wednesday, January 28, 2009

A histogram is a graph of a frequency distribution and is a useful way to give a picture summary of a set of data involving a quantitative variable. In this activity, you will create and interpret histograms.

1. How is a histogram similar to a bar graph and how is it different from a bar graph?

The following table gives the percentage of high school seniors who took the SATs in the academic year ending in 2006 for a group of 15 southeastern states and Washington DC.

2. What is the range of the “percent taking test” data shown in the table?

3. If you want to group the data into approximately six classes, what intervals could you use?

4. Why is it important to group the data?

5. Why do you want to choose intervals of equal width?

On a separate sheet of paper, which you do not need to turn in, create a table with six "bins" (or intervals), and then create the associated histogram.

7. Describe the overall shape of the histogram which you just created "by hand."

8. There are several ways to create a histogram using Excel. We'll illustrate the FIRST way using the SAT data file for all states, EA1.3.1 SAT data.xls.

9. Describe the shape of the SAT histogram for all states. How does it compare to the histogram for the southeastern states? Using the two histograms, what can you say about the percentage of seniors taking SATs in the southeastern states and in all states?

10. Here is a SECOND method to create a histogram with Excel. For this histogram, you'll use a file containing data about the points scored by the winning team in the Super Bowl for the years from 1967 to 2008. Retrieve the file, EA1.3.2 Super Bowl.xls. You will make one histogram with bins determined by Excel (steps a-d in the directions below), and the other will use bins you enter (steps e-f in the directions linked below).

Note: the data range in the directions below is given as B1:B38, but since we are using updated data, the range of cells that you will use is different.

11. Explain what the histogram shows about points earned by Super Bowl winning teams.

Summary
In this activity, you grouped data to create histograms by hand and using Excel. With Excel, you created histograms in two different ways: as a bar graph using the frequencies you computed and then adjusting the width of the bars so that there were no gaps in between them, and as a histogram using the histogram function in Excel, in which frequencies are computed automatically.