Dropping Lowest Grades

Many teachers allow students to drop the lowest score from a sequence of quizzes, tests, or homework assignments. When the number of grades is large, some teachers will even allow students to drop several of their lowest scores. A computer gradebook program would need to implement an algorithm to provide this feature (see one of many examples of computer gradebook software, for example, [4]). A natural criterion to decide which grades to drop would be to drop the set of grades that maximizes the student’s final grade. In some circumstances, it can be non-trivial to determine the best grades to drop. Using natural brute force methods, the time needed to find this optimal set of grades to drop can grow exponentially as the number of grades involved grows making these methods impractical even on fast computers. We discuss some unexpected behavior exhibited by this problem and provide a simple and very efficient algorithm for finding the best set of grades to drop.