ACTIVITY 16-1 Visualizing Football Scores: Measures of Center and Spread 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. 1. The following table gives the points scored by the Philadelphia Eagles in their sixteen 2010–2011 regular season games: Date Points Scored- Eagles 12-Sep 20 19-Sep 35 26-Sep 28 3-Oct 12 10-Oct 27 17-Oct 31 24-Oct 19 7-Nov 26 Activity 16-1: Visualizing Football Scores: Measures of Center and spread 459 Instructions to Find the Mean and Median of a List of Data 1. In cell A19, type the word mean, and in cell A20 type the word median. 2. In cell B19, instruct Excel to calculate the average (that is, mean) points scored by entering the command =average(B2:B17); in cell B20, calculate the median points scored by entering the command =median(B2:B17). e. Record the average and median points scored per game by the Eagles in 2010-2011 here: average median Describe how these values compare with your estimate of the "center" of this data set in Question 1(a). f. 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 to give the range of the data; that is the maximum score) - (the minimum score) = (max) - (min). Give the range of the Eagles football data here: (This shows the spread of the data, but may be misleading if one or both of these values are outliers.) 8. To get a better sense of the spread, you'll now look at the quartiles. The first quartile, denoted Qı, is the median of the lower half of the data values.* The third quartile, denoted Q3, is the median of the upper half of the data values. The fol- lowing list of numbers is the five-number summary of a data set: minimum, Q1, median, Q3, maximum. Use Excel to find Q, and Q3 for the data set of Eagles' *Note that some texts and software give slightly different descriptions of how to find the first and third quartiles. Excel contains a built-in function QUARTILE that could also be used to find the quartiles. In this activity, you are asked to find quartiles using the description of quartiles as medians of subsets of the data, because doing so helps enhance understanding of what quartiles represent. 460 Topics points scored by using the median command and the appropriate halves of the data for each. Record the five-number summary of this data set: h. Sketch a boxplot for this data set in the space provided. 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. 2. The following table gives the points scored in the 2010–2011 regular season games by the Washington Redskins and the N.Y. Giants teams: Points Scored- Points Scored- Date Giants Date Redskins 12-Sep 31 12-Sep 13 19-Sep 14 27 26-Sep 10 19-Sep 26-Sep 3-Oct 16 3-Oct 17 17 10-Oct 34 10-Oct 16 17-Oct 28 17-Oct 24 25-Oct 41 24-Oct 17 41 31-Oct 25 7-Nov 14-Nov 21-Nov 20 15-Nov 28 17 21-Nov 19 28-Nov 24 28-Nov 13 5-Dec 31 5-Dec 7 13-Dec 21 12-Dec 16 19-Dec 31 19-Dec 30 26-Dec 17 26-Dec 20 2-Jan 17 2-Jan 14 a. Look at the “points scored” by each team and estimate the "center" of the data for each data set. Your estimate of "center” for the Giants: Your estimate of "center" for the Redskins: 458 Topics 15-Nov 59 21-Nov 27 28-Nov 26 2-Dec 34 12-Dec 30 19-Dec 38 28-Dec 14 2-Jan 13 Source: National Football League, www.nfl.com. a. Without doing any computations, look at the “points scored" values and estimate the "center” of the data set. Why did you choose this value? b. 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. c. Sort the data by “points scored” (in ascending order) and find the median number of points scored; write it here: d. Use the following Excel instructions to find the mean and median points scored by the Eagles in 2010–2011. Activity 16-1: Visualizing Football Scores: Measures of Center and Spread 461 b. Retrieve the file "EA16.1 Points Scored 2010 2011.xls” (which contains the data shown in the previous tables) from the text website or WileyPLUS website, or enter the data into Excel for the New York Giants and Washington Redskins NFL teams. C. Find the five-number summary for points scored by each of these teams and record them here. Giants: Redskins: d. Go to www.nfl.com/teams and click the "Stats” link below the team you want, to get the most recently completed season points scored for one additional NFL team. Find the five-number summary for your team and sketch comparative boxplots showing the five-number summaries for points scored by the Eagles and the three additional football teams on the same scale. e. Write a paragraph describing what these four comparative boxplots show about the scores of the four NFL teams. Who do you think would win a game between the Eagles and Giants? Explain your reasoning. Who do you think would win the other five games that could be played between pairs of these four teams? 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 performances of four different football teams.
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