# Flaws of Averages

Length: 5 weeks
Subject Areas: Mathematics, Engineering

## Overview

Welcome to an exciting learning experience for your students and for you!  This multi-week Project-Based Learning (PBL) unit focuses on averages, what they mean and how they can be misleading.  We want the students to become sophisticated “consumers” of any and all documents or conversations that use the term “average,” always knowing what follow-on questions to ask in order to assure full understanding.

## Sequence of Project Activities

• Students will start by watching and discussing the MIT BLOSSOMS video lesson, Flaws of Averages, insuring that they understand the concepts presented.
• Students will look for examples of the use of averages in newspapers and on TV, and attempt to decide whether the use of the Average was appropriate or not.
• Teacher will lead a discussion on what information may be lost when one only considers Averages and what additional data one must look at to get a truly insightful picture.
• Teacher will present a lesson on Histograms and Distributions, explaining what information each provides and helping students learn to identify whether any given example is an effective use of averages or not.
• Students working in teams of four will do a warm-up exercise to their longer project, collecting one week of data and creating a histogram of it – identifying the mean, the median and the mode.
• Student Teams will work on their Community Safety Projects, designing the data collection strategy and developing an implementation plan for that strategy.
• After data collection is completed, Student Teams will work to assemble and integrate the data, display it in a histogram, compute mean, mode and median, ultimately making inferences from the data that could benefit their community.
• Each Student Team will write up a 10-page report of their findings, with presentation slides including histogram, photographs and ameliorative suggestions to potentially present to an appropriate community professional.
• Each Student Team will present their findings as described above to a public audience at their school during the Final Event.

### Summative Assessment

*Teacher Note: Having Student Teams meet with community professionals is preferable, but optional for this project.