The Flaws of Averages
From Richard C. Larson
The most popular MIT BLOSSOMS video lesson is “Flaws of Averages,” created and performed by Ms. Rhonda Jordan and Mr. Dan Livengood, now both with Ph.D.s from MIT. See http://blossoms.mit.edu/videos/lessons /flaws_averages, available in four languages! The idea of this video can be placed in front of students at almost any level, say from 6th grade upwards, where the teacher can ask the students to think of other Flaws of Averages and report them back to the class. The idea is to get the students to think about averages in their everyday lives, how averages assist in our understanding and how they can be misleading. This gets STEM thinking outside of the classroom and into everyday experiences. It should engage the students for many hours.

The teacher might illustrate with simple examples, formatted for younger audiences: (1) When a hi-tech very rich person (billionaire) mom or dad enters a playground with her/his child, on average all parents in the playground become millionaires! Does this aid in your understanding of the situation? Or is this a confusing and misleading application of averages? Then there is the famous example from Garrison Keillor's Lake Wobegon radio program: "Lake Wobegon, where all the children are above average." Lake Wobegon is a fictional town in Minnesota, USA. The students should discuss this: Impossible or possible? And, Why?

In everyday life: (a) Two students flip a fair coin to see which one will get the one candy-bar for dessert. On average each student’s winnings equal one half of a candy-bar, an impossible outcome. So, the lesson here is that the average in a situation may be impossible to experience. (b) You go out jogging, which includes sprints as well as slower regular jogging. How do you estimate your average speed in miles per hour? (c) You have a smart phone that you carry with you. Over your waking hours, determine the X-Y coordinates of your average location today in your community. Does the answer aid or distract from insight and intuition? (d) As a student you commute to school on public transportation, a bus or a subway. You have collected some data on the average time between bus or subway arrivals at your station. It’s ten minutes. So, you think that your average wait time for a bus or subway would be half of that, five minutes. But over a month of data collection, you find that it’s much higher, 9.5 minutes, and yet average time between two successive busses or subways remains ten minutes. Why? How is this possible?

And so on. This could be a fascinating STEM math project lasting for months in any classroom.

Richard Larson is the Mitsui Professor of Engineering Systems at MIT. He is also the Director of MIT LINC and the Principal Investigator of MIT BLOSSOMS.

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