Park City Mathematics Institute
Data, Statistics, and Probability

Was Leonardo Correct? (continued)
by Aaron Orzech, Joe Gonzales, and Todd Smallcanyon


zipped folder with all files:

General Files
    Correspondence of Data
        MS Word | PDF format
    Data Sets
        Excel | Excel zipped

Teacher Training Module Files
    MS Word | PDF format

Body Measurements Files
    Teacher Notes: PDF format
    Student Instructions: MS Word | PDF format
    Student Worksheets: MS Word | PDF format
    ANSUR Average Value
        Fathom | Fathom zipped

Perfect Face Files
    Teacher Notes: MS Word | PDF format
    Student Data: Fathom | Fathom zipped


The three activities included here are:

  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)

This could be used with an advanced Algebra 1 class, or for a pre-AP Statistics class. Concepts used include ratios, measures of central tendency, percentiles and least-squares regression. Topics alluded to but not explicitly discussed include the Normal distribution and sampling methods.


Rulers or tape measures (or calipers of various sizes if available), copies of student worksheets and student instructions, computers equipped with Fathom™ software.

  • Collect a small sample of data, and consider its relationship to data about a larger population.
  • Use percentiles, measures of central tendency, and other methods to examine relationships and distributions in a data set.
  • Use appropriate statistical tools and vocabulary to examine the question of what is typical, and to make comparisons between items in a data set.

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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
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

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.