Park City Mathematics Institute
Reasoning from Data and Chance
Project Abstract

Drafts of Project Files (password required)

Data Exploration of 2000 Census NY Income Data
Timon Holman* and Huong Nguyen
This lesson is meant to introduce students with minimal prior exposure to data exploration. Students are given a sample of real Census Bureau data (from 2000) related to income and educational achievement. Students are guided in examining the actual cases and looking for unusual or interesting cases. Then the students are asked to build dot plots, histograms, and box (box & whisker) plots as a method for examining the data. Next, students are asked to use the internet to collect 4 subsamples (size 100) from the original Census data (size 1658). For each of these they use Fathom to create summary plots and summary statistics. Students then examine the variability between these samples. Finally, students examine the relationship between income and educational attainment. We hope students conclude finishing high school and further education has a high payoff. This lesson can lead to many additional explorations which examine the factors impacting income.
Was Leonardo Correct? (continued)
Aaron Orzech*, Joe Gonzalez, Todd Smallcanyon
These activities build on "Least-Squares Lines and Correlation - Was Leonardo Correct?" from Exploring Statistics with Fathom, which examines the accuracy of various ideal ratios between body measurements that Leonardo da Vinci prescribed during the Renaissance. They do not assume, or require, access to or familiarity with that activity. They extend the original activity by asking students to compare different ways of describing relationships and of measuring what is "typical" in a population. Students will examine the use of Least-Squares lines, mean, median and percentiles to identify typical ratios between different anthropometric measurements. These activities assume some familiarity with interpreting the slope and intercept of a line in context, and provide an entry point to discussing percentiles and distributions, particularly the Normal distribution. This activity also offers the possibility of extending the discussion to sampling, by offering a very large collection (3982 cases, taken from ANSUR, the U.S. Army Anthropometry Survey) from which samples of different sizes and compositions can be drawn to test for accuracy and bias.
  1. A teacher training module for teachers just learning how to use Fathom software (Teacher Training Module, contact Joe Gonzales)
  2. An activity studying the ratios between different body measurements (Body Measurements, contact Aaron Orzech)
  3. An activity studying the ratios between different head and face measurements, which could be used to extend the concepts in Body Measurements, as a standalone activity, or in conjunction with an art class (Perfect Face, contact Todd Smallcanyon)
Rigged or Fair?
Kent Hansan* and Richard (Matt) McLarney
This series of two lessons allows students to examine what would qualify a game as rigged through two hands on experiments and comparing individual and class results to expectations. The conclusions of the class can then be tested by comparing them with thousands of trials for each situation simulated by Fathom. On the second day, students will work in groups to apply what they learned from the day before to new situations where they already have the results of a game.
Can you "see" the difference?
Oscar Chavarria* and Vicki Lyons
This is an exploration of the usefulness of the F statistic in detecting the difference in the means of treatment groups. Following an example from Stats Modeling the World, Fathom is used to look at what happens when variances within treatment groups are changed. Typically, as the within treatment variance increases it becomes more difficult to detect differences in the treatment means. This difference is formally measured with the ratio of the variance between treatment means to the variance within treatments.

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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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.