Activity 16.1

Visualizing Football Scores: Measures of Center and Spread

10 points

Due at the beginning of lab, Tuesday, April 7, 2009

In this activity, you will examine some data from the National Football League and investigate several numerical measures of center and spread and a graphical method particularly useful for comparing data sets.

The following table gives the points scored by the Pittsburgh Steelers in their 16 regular season games during the 2008 season. (Source: http://www.nfl.com/teams ).

1. Without doing any computations, look at the "points scored" values and estimate the "center" of the data set. Why did you choose this value?

2. Enter the dates and points scored and the column titles, as they appear in the table, into columns A and B of an Excel worksheet.

3. In Excel, sort the data by "Points Scored," in ascending order. By inspecting the data (no formula yet), determine the median value of the data and enter it in your Word document.

4. Use the following Excel instructions to find the mean and median points scored by the Steelers in 2008, and enter these values into your Word document. Also, describe how these values compare with your estimate of the "center" of the data in #1.

Instructions to Use Excel to Find the Mean and Median of a List of Data
- In cell A19, type the word mean, and in cell A20 type the word median.
- In cell B19, instruct Excel to calculate the average (that is, mean) points scored by entering the command = average(B2 : B17)
- In cell B20, and calculate the median points scored by entering the command = median(B2 : B17)

5. Looking at the center of a distribution doesn't give the whole picture; you might also want to measure the spread of the data. One way to do this is with the range of the data; that is, maximum - minimum.

What is the range of the Steelers' scores above?

Note that range might be misleading if one, or both, of the extreme values are outliers.

6. To get a better sense of the spread, we'll consider quartiles. The first quartile, denoted Q₁, is the median of the lower (smaller) half of the data. The third quartile, denoted Q₃ , is the median of the upper half of the data values. These are part of the five-number summary of a data set:

(1) minimum
(2) Q₁
(3) median
(4) Q₃
(5) maximum

Use Excel to find Q₁and Q₃ for the Steelers' points-scored data, by using the median command and the appropriate halves of the data for each. (Note that there might be easier ways to calculate the quartiles in Excel, but this approach helps enhance the understanding of what quartiles represent.) Enter the five-number summary in your Word document.

7. On a separate sheet of paper, which you do not need to turn in, sketch a boxplot for this data set. First, set up a horizontal axis. Next, mark a scale on your axis, then locate each of the five numbers in the five-number summary on the axis, and complete the boxplot.

8. The following table gives the points scored in the 2008 regular season games by the Philadelphia Eagles and the Cleveland Browns. Look at the "Points Scored" by each team and enter your estimate of the "center" of the data, for each, into your Word document.

The file EA16.1 Points Scored 2008.xls contains the above data. Copy and past this data into the Excel spreadsheet you've been using.

9. Calculate the five-number summary for points scored for both the Eagles and the Browns, and enter this into your Word document.

10. Based on your five-number summaries for each team, predict an outcome if these teams played against each other. Please give a thorough explanation. Then go to http://www.nfl.com/teams and determine whether these teams played in 2008 (including playoffs...), and what actually happened if/when they did play.

Summary
In this activity, you used Excel to calculate mean and median. You found the five-number summary for several data sets of football scores. You also drew boxplots and used them to compare the performance of different football teams.