Park City Mathematics Institute
Data, Statistics, and Probability

Biased Rectangles?
by Carol Hattan, Beverly Farahani, David Kapolka, Marie Lusk,
David Hernandez, Patricia Daniel & Cheryl Foox

Go to: overview
Download: MS Word file

This classroom activity is an adaptation of a lesson from the NCTM Navigating through Data Analysis in Grades 9-12, chapter 1, to be used with Fathom© rather than a graphing calculator. The original "100 rectangles" sheet (Random Rectangles) comes from Activity-Based Statistics, Key College Publishing.

AP Statistics, Secondary Statistics, Pre-Calculus, and possibly Algebra II

1 to 2 class periods

   Fathom software
   Fathom file: download [Mac]  [PC]
   Fathom Activity Guide (Fathom 1) download [MS Word] or view [HTML]
   Fathom Activity Guide (Fathom 2) download [PDF format] or [MS Word]
   100 rectangles

Students explore one example of how bias affects the mean. This simulation increases students' understanding of the significance of sample size on the calculation of the mean.

Exploring this concept allows teachers and students to consider ideas such as:

  • How does a randomly generated sample compare with a human sample?
  • What happens to the shape and spread of the graph of the data as the sample size increases?
  • What do you see when comparing a normal curve to the shape and spread of a histogram of the sample data? (extension)

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.