**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. |