D. Legault, Minnesota Literacy Council, 2014
The Typical Super Bowl Score? Name_____________________________
How many points will be scored this Super Bowl? Round to the nearest hundredth when necessary.
To get a clearer idea lets look at the last twelve Super Bowl scores:
XLVII Feb. 3, 2013 Ravens 34, 49ers 31
XLVI Feb. 5, 2012 Giants 21, Patriots 17
XLV Feb. 6, 2011 Packers 31 Pittsburg 25
XLIV Feb. 7, 2010 Saints 31 Colts 17
XLIII Feb. 1, 2009 Pittsburgh 27 Arizona 23
XLII Feb. 3, 2008 New York 17, New England 14
XLI Feb. 4, 2007 Indianapolis 29, Chicago 17
XL Feb. 5, 2006 Pittsburgh 21, Seattle 10
XXXIX Feb. 6, 2005 New England 24, Philadelphia 21
XXXVIII Feb. 1, 2004 New England 32, Carolina 29
XXXVII Jan. 26, 2003 Tampa Bay 48, Oakland 21
XXXVI Feb. 3, 2002 New England 20, St. Louis 17
1. What is the mean score for the winning team in the Super Bowl? Make sure to show or explain your method.
(34+21+31+31+27+17+29+21+24+32+48+20) /12 = 335 /12 = 27.92
2. What is the mean score for the losing team in the Super Bowl? Make sure to show or explain your method.
(31+17+25+17+23+14+17+10+21+29+21+17) / 12 = 242 / 12 = 20.17
3. By using the mean of the winning and losing scores, what is the mean Super Bowl final score? By how many
points on average does the winning team beat the losing team by?
Mean of the winning and losing scores = (27.92 + 20.17) / 2 = 24.05
Differences between the winning and losing scores are; 3, 4, 6, 14, 4, 3, 12, 11, 3, 3, 27, 3. The mean of
those differences if 93/12 = 7.75
4. Find the median score of the winning teams in the Super Bowl. Make sure to show or explain your method.
17 20 21 21 24 27 29 31 31 32 34 48
= winning scores arranged from smallest to largest.
So, the median winning score is 27 + 29 = 56/2 = 28.
5. Find the median score of the losing teams in the Super Bowl. Make sure to show or explain your method.
10 14 17 17 17 17 21 21 23 25 29 31
= losing team scores arranged from smallest to largest.
So, the median losing score is (17+21)/2 =19.
6. By using the median of the winning and losing scores, what is the median Super Bowl final score? Using the
median, by how many points on does the winning team beat the losing team by?
Maybe the median final Super Bowl score would be the average of 28 and 19 which is 28 + 19 = 47/2 =
23.5. The winning team usually wins by 28 – 19 = 9 points.
7. Now that you have used both the mean and median to explore the typical Super Bowl score, which statistic
seems to better represent the data? Why?
I’m not sure that either is more representative. The median losing team score is a score that is much closer
to the lowest losing score than the highest losing score. There are also 4 losing scores of 17. So the mode
is 17 and 19 is pretty close to the mode. The mode of 17 makes the median values weighted more heavily
in the 17 score.
8. Looking at all scores, winning or losing, is there a mode of the data set? If so, what is it? Knowing what you
know about football, does it make sense that this score would be the mode?
17 appears in the losing scores four times and once in the winning scores. It appears a total of five times
making it the only mode.
9. Another statistic that we have not talked about is the range. Find the range for each:
a. Which of the twelve Super Bowls had the greatest range? Which Super Bowl was that and what was the
range?
Tampa Bay 48, Oakland 21 range = 27 points
Super Bowl 37 = XXXVII
b. Find the range of the scores of the winning Super Bowl teams.
17 to 48 = 31 points
c. Find the range of the scores of the losing Super Bowl teams.
10 to 31 = 21 points
d. Find the range of all of the Super Bowl scores from the data set.
10 to 48 = 38 points
10. Next year we will add the 2014 Super Bowl score to this data set. How many points will the 2014 losing team
need to score so that the new 13 year mean of the losing scores is exactly 20 points? How many points will the
winning team need to score so that the 13-year mean is exactly 30 points? Show or explain your method.
Total losing team scores of the 12 games = 242. If we want the new mean score with 13 games to = 20
then we need for the total of the scores to = 20 x 13 = 260 points. This year’s losing team would have to
score 260 – 242 = only 18 points.
To have a mean score of 30, the total of the winning team scores would have to = 13 x 30 = 390. The total
now of the winning team scores is 335. So, to have the 13-year mean become 30 points, this year’s
winning team would have to score 390 – 335 = 55 points.
11. If the 2014 Super Bowl score is 3 – 0, will that have a greater effect on the mean Super Bowl score or the
median Super Bowl score? Show or explain your reasoning.
Mean super bowl score was = total of the winning scores and the losing scores for 12 games is 335 + 242 =
577 and that represents 24 team scores. When we add the 3 + 0 scores to the list we get 580 representing
26 team scores. The mean would = 580 / 26 = 22.31. So the previous mean team score of 24.05 is changed
by almost 2 points.
To figure out the new median, we could list all of the scores from smallest to largest.
0 3 10 14 17 17 17 17 17 20 21 21 21 21 23 24 25 27 29 29 31 31 31 32 34 48
The new median score would be 21. Which is slightly lower than the calculated median of all of the
previous scores of about 23.5. That makes sense because the two scores that we just added to the list were
the lowest scores in the series. It looks like the median score of all of the games scores is slightly more
affected than the total mean score.
Source for data: http://www.superbowlhistory.net/superbowl/scores.php
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