Article from: The UMAP Journal Fall 1998 pages 323-327

Judge's Commentary
The Outstanding Grade Inflation Papers

Grade point average (GPA) is the most widely used summary of undergraduate student performance. Unfortunately, combining student grades using simple averaging to obtain a GPA score results in systematic biases against students enrolled in more rigorous curricula, and/or taking more courses. An example from Larkey of four students (call them I-IV) in which student I always obtains the best grade in every class she takes and IV always obtains the worse grade in every class he takes, yet student I has a lower GPA than student IV does, is as follows:

  Student I Student II Student III Student IV Class GPA
Class 1 B+     B- 3.00
Class 2 C+   C   2.15
Class 3     A B+ 3.65
Class 4 C- D     1.35
Class 5   A   A- 3.85
Class 6 B+     B 3.15
Class 7   B+ B   3.15
Class 8 B+ B B- C+ 2.83
Class 9   B B-   2.85
Student GPA 2.78 2.86 2.88 3.0  

The MCM problem was to determine a ``better'' ranking than one using pure GPAs; this problem has no simple ``solution''. A recent paper by Johnson [1] refers to many studies of this topic, and suggests a technique that was considered, but not accepted, by the faculty at Duke University in North Carolina.

Each of the participating schools is to be commended for its efforts in tackling this problem. As in any open-ended mathematical modeling problem there is not only great latitude for innovative solution techniques but also the risk of finding no results valuable in supporting one's thesis. Solutions submitted contained a wide variety of approaches including graph theory and fuzzy logic.

Unfortunately, several teams were confused as to the exact problem the Dean wanted solved. Assigning students to deciles, by itself, was not the problem. For example, deciles could be assigned by obtaining a list of student names, and choosing the first 10% of the students to be in the first decile, etc. What the Dean wanted was meaningful students deciles, based on students' relative class performance. Simply re-scaling GPA's such that the average became lower (and the top 10% became more spread out) would not change the inherent problem.

The problem statement suggested that relative rankings of students within classes should be used to evaluate student performance. With this assumption, possible approaches include:

In the latter case (which was chosen by most teams), an instructor who assigns A's to all students in a class provides exactly the same information as an instructor who assigns all C's to the same students when enrolled in another class.

Specific items that the judges looked for in the papers included:

None of the papers had all of the components mentioned above, but the outstanding papers had many of these features. Specifics pluses of the outstanding papers included:


Valen E. Johnson, ``An Alternative to Traditional GPA for Evaluating Student Performance'', Statistical Science, 1997, Vol. 12, No. 4, pages 251-278.

About the Author

Daniel Zwillinger attended MIT and Caltech, where he obtained a PhD in applied mathematics. He taught at RPI for four years, worked in industry for several years (Sandia Labs, JPL, Exxon, IDA, MITRE, BBN), and has been managing a consulting group for the last five years. He has worked in many areas of applied mathematics: signal processing, image processing, communications, and statistics. He is the author of several reference books in mathematics.