Averages: Still Flawed
Averages: Still FlawedEnglish
St. Louis, MO
This learning video continues the theme of an early BLOSSOMS lesson, Flaws of Averages, using new examples—including how all the children from Lake Wobegon can be above average, as well as the Friendship Paradox. As mentioned in the original module, averages are often worthwhile representations of a set of data by a single descriptive number. The objective of this module, once again, is to simply point out a few pitfalls that could arise if one is not attentive to details when calculating and interpreting averages. Most students at any level in high school can understand the concept of the flaws of averages presented here. The essential prerequisite knowledge for this video lesson is the ability to calculate an average from a set of numbers. Materials needed include: pen and paper for the students; a blackboard or equivalent; and coins (one per student) or something similar that students can repeatedly use to create a random event with equal chances of the two outcomes (e.g. flipping a fair coin). The coins or something similar are recommended for one of the classroom activities, which will demonstrate the idea of regression toward the mean. Another activity will have the students create groups to show how the average number of friends of friends is greater than or equal to the average number of friends in a group, which is known as The Friendship Paradox. The lesson is designed for a typical 50-minute class session.
Dan Livengood completed his Ph.D. in 2011 from MIT’s Engineering Systems Division. He is currently teaching as an Adjunct Lecturer at Washington University in St. Louis. He is also spending time as an entrepreneur with a systems engineering startup firm focusing on healthcare and social services.
Rhonda Jordan earned her Ph.D. in 2013 from MIT's Engineering Systems Division. She is currently an Energy Specialist at the World Bank, working in the areas of power planning, energy access, renewable energy integration, and smart grid applications.
- Regression Toward the Mean and the Binomial Distribution (Supplement for the break after the third segment) (PDF)
- The Friendship Paradox (Supplement for the break after the fourth segment) (PDF)
- The Fishing Competition (Supplement for the break after the fifth segment) (PDF)
- Wind Turbine on your Island Homework Problem (PDF)
Additional Online Resources
An interesting article in the New York Times on the “Lake Wobegon Effect”.
This resource, provided by the National Education Association, presents the six-part math series, “ ME, Myself and I”, that looks at us and our place in the Cosmos mathematically. The series includes a section on “The Friendship Paradox”.
This is a second piece from the New York Times -- this time on “The Friendship Paradox”.