# 1998 MCM B： Grade Inflation

#### Background

Some college administrators are concerned about the grading at A Better Class (ABC) college.  On average, the faculty at ABC have been giving out high grades (the average grade now given out is an A-), and it is impossible to distinguish between the good and mediocre students.  The terms of a very generous scholarship only allow the top 10% of the students to be funded, so a class ranking is required.

The dean had the thought of comparing each student to the other students in each class, and using this information to build up a ranking.  For example, if a student obtains an A in a class in which all students obtain an A, then this student is only “average” in this class.  On the other hand, if a student obtains the only A in a class, then that student is clearly “above average”.  Combining information from several classes might allow students to be placed in deciles (top 10%, next 10%, etc.) across the college.

#### Problem

Assuming that the grades given out are $(A+, A, A-, B+, . . . )$ can the dean’s idea be made to work?

Assuming that the grades given out are only $(A, B, C, . . . )$ can the dean’s idea be made to work?

Can any other schemes produce a desired ranking?

A concern is that the grade in a single class could change many student’s deciles.  Is this possible?

#### Data Sets

Teams should design data sets to test and demonstrate their algorithms. Teams should characterize data sets that limit the effectiveness of their algorithms.