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.
(Accessed at http://athletics.mountunion.edu/sports/fball/2012-13/roster, http://www.rolltide.com/sports/m-footbl/mtt/alab-m-footbl-mtt.html on 1/14/13)
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 |
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."
"This difference in average weights is approximately ____________ of either team"
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 realtive 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 inthe data sets.