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MATH104 Moravian College Measures of Center and Spread Football Scores Excel Worksheet
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Mathematics
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Moravian college
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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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