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# Offensive Linemen

Alignments to Content Standards: 7.SP.B.3 7.SP.B.4

College football teams are grouped with similar teams into "divisions" (and in some cases, "subdivisions") based on many factors such as game attendance, level of competition, athletic department resources, and so on. Schools from the Football Bowl Subdivision (FBS, formerly known as Division 1-A) are typically much larger schools than schools of any other division in terms of enrollment and revenue. "Division III" is a division of schools with typically smaller enrollment and resources.

One particular position on a football team is called "offensive lineman," and it is generally believed that the offensive linemen of FBS schools are heavier on average than the offensive linemen of Division III schools.

For the 2012 season, the University of Mount Union Purple Raiders football team won the Division III National Football Championship while the University of Alabama Crimson Tide football team won the FBS National Championship. Below are the weights of the offensive linemen for both teams from that season.

Alabama
277
265
292
303
303
320
300
313
267
288
311
280
302
335
310
290
312
340
292
Mount Union
250
250
290
260
270
270
310
290
280
315
280
295
300
300
260
255
300

1. Based on visual inspection of the dotplots, which group appears to have the larger average weight? Does one group seem to have greater variability in its weights than the other, or do the two groups look similar in that regard?
2. Compute the mean and mean absolute deviation (MAD) for each group. Do your measures support your answers in part (a)?
3. Choose from the following to fill in the blank: "The average Alabama offensive lineman's weight is about __________ than the average Mount Union offensive lineman's weight."

1. 20 pounds lighter
2. 15 pounds lighter
3. 15 pounds heavier
4. 20 pounds heavier

"This difference in average weights is approximately ____________ of either team."

2. Slightly more than 1 MAD
3. Twice the MAD
4. The offensive linemen on the Alabama team are not a random sample from all FBS offensive linemen. Similarly, the offensive linemen on the Mount Union Team are not a random sample from all Division III offensive linemen. However, for purposes of this task, suppose that these two groups can be regarded as random samples of offensive linemen from their respective divisions/subdivisions. If these were random samples, would you think that offensive linemen from FBS schools are typically heavier than offensive linemen from Division III schools? Explain your decision using answers to the previous questions and/or additional analysis.

## IM Commentary

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale. Since the two distributions have similar variability and almost identical MADs, students are able to express the difference in mean values with reference to the MAD of either group. As a possible extension, students can investigate if these distributions are in fact similar to the distributions of offensive lineman weights at similar schools (such as schools in the same respective divisions or conferences).

Task 1340 is similar to this task, and looks at heights of players from two different sports. In that task, the difference in MAD's is also about 2. However, in that task variability for the two groups was judged as different because a difference of 2 inches is large relative to the height values, which range from 62 to 79 inches. In this task, where the weights range from 250 to 340, a difference of 2 pounds is judged as not meaningful, relative to the weight values in the data sets.

## Solution

1. The center of the Alabama distribution is much higher on the number line than the center of the Mount Union distribution, so at first glance, it appears that the Alabama group has the higher average. The values for the Alabama distribution appear to have a spread and general concentration that is very similar to the Mount Union distribution, so we would conjecture that the distributions' spread measures would be rather similar.
2. Alabama mean = 300, MAD = 15.68; Mount Union: mean = 280.88, MAD = 17.99
3. D (20 pounds heavier); B (Slightly more than 1 MAD)
4. Yes, it appears that offensive lineman from such FBS schools such as Alabama are typically heavier than Division III offensive linemen. In addition to any arguments/statements made earlier regarding the dotplots and summary measures, one could also mention that only 2 of the 17 Mount Union offensive linemen were above the average of the Alabama distribution, only 3 of the 19 Alabama offensive linemen are below the Mount Union average, and similar comparative arguments.

#### Renee says:

8 months

Thanks for the additional questions Dave! I love being able to help students see how this math can be used in the real world!

#### David says:

over 3 years

I gave the kids the following scenario (not found in the activity), although it requires a brief discussion to build prior knowledge for those not already familiar with football:

You are the Assistant Coach in charge of the Offensive Line. The Head Coach has asked you for a list of players that need nutritional counseling and/or more time spent with the athletic trainer in the gym.

How will Mean Absolute Deviation help you select the correct players? Identify those players below the average range of weight that need to increase their size through diet and exercise that you would require to attend. Identify those players above the average range of weight that might need to decrease their size through diet and exercise that you would require to attend. Why might you not refer certain offensive lineman that are above the average range? What other data might you look at before deciding whether or not to refer a lineman above the average range? Are there any other players you might invite to improve your team besides those required to attend already? Who would they be?

Just a thought if anyone finds it helpful; I welcome any feedback if I am missing something or seeing it incorrectly.

Thanks for the resource, Dave