Reverse Engineering GPA Distributions from Honors Data

Sometimes universities decline to publish the distribution of grade point averages (GPAs) of their students. Such schools often publish, however, the grade point averages attained by students at various levels of "honors". The school might say, for example, the top 30% of students had GPAs of at least 3.3 and the top 15% of students had GPAs of at least 3.5. This Demonstration shows how the overall distribution of GPAs can be reverse engineered from such honors data. You select two data points to correspond with two levels of honors. The Demonstration responds with its best estimate of the cumulative distribution function of grades.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The Demonstration uses the prevailing American calibration of grades, which requires them to lie between 0 (an "F") and 4 (an "A").
The Demonstration assumes, incorrectly, that GPAs are normally distributed. In fact, this is unlikely to be the case. GPAs are calculated as the mean of draws from an underlying censored distribution. The underlying distribution is censored because, generally speaking, grades cannot exceed a maximum value (such as 4.0) or go below a minimum value (such as 0). The mean of these draws must, therefore, itself be censored to lie between the minimum and maximum values. Still, some experimentation suggests that the assumption that GPAs are normally distributed does not generally result in large errors.
The idea for this Demonstration is suggested in Ian Ayres, Super Crunchers, New York: Bantam Dell, 2007.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+