Flaws of Averages

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Driving Question

How to better understand Averages: what information are they giving us and in what ways may they be misleading us?

Big Idea

The “Tyranny of Averages” refers to the idea that group averages fail to impart the whole story of data because averaging flattens otherwise jagged information to a single point, thus leaving out important details and variations within the data. In this PBL, student teams will collect data from their communities, create a histogram and distribution of that data, analyze the mean, medium and mode and report their findings to a relevant community official, with suggestions for ameliorative actions. One important goal of this project is to make students more knowledgable and skeptical consumers of statistics. 

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Student Entry Event

<p><strong>Rhonda L. Jordan </strong>is a Ph.D. student in the Engineering Systems Division at MIT and is interested in sustainable energy development in developing economies.&nbsp;</p> <p><strong>Daniel J. Livengood</strong> is a Ph.D. student in the Engineering Systems Division at MIT and is interested in how the evolution of the electric grid will incorporate responsive electricity demand to help manage the grid most efficiently, especially as weather-dependent sources of electricity supply (such as wind
MIT BLOSSOMS Video Lesson
Flaws of Averages

Students Will Learn

  • About many situations in which focussing only on the average of a data set can distort the reality of that data
  • About Histograms and how to construct them 
  • About Distributions and what they tell us
  • The definitions of the mean, medium and mode 
  • About the role of data outliers
  • About safety issues in their own communties
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Students Will Be Able To

  • Distinguish between situations where the use of averages is effective and those where one needs to think in terms of distributions, not only averages
  • Collaborate with team members to design an effective data collection strategy on important safety issues in their community
  • Analyze that data by constructing a Histogram and Distribution of it
  • Write up report on the findings and present that report to relevant community officials
  • Prepare and present a presentation on their findings to a large audience
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