# Is this an improper method of averaging grades? If so, what is a simple mathematical way of explaining it?

I have a professor who employs a unique method of averaging grades.

On each assessment, the professor assigns a raw numerical score to each student based on performance. He then converts particular ranges of numerical scores into letter grades.

For example, on the first assessment, students were graded out of 18. Those who received 16.5-17 got an A-, 15-16 a B+, 11.5-14 a B, 7.5-11 a B-, etc. On the second assessment out of 10, students who received 8-10 got an A, 3-7 a B, and 0-3 a C.

Near the end of the course, the professor told the class that he would determine the final letter grade in the course by calculating a weighted average of the letter grades rather than the raw numerical scores for each assessment. In this calculation based on the GPA equivalent for letter grades employed by my university, an A is a 4.0, A- a 3.7, B+ 3.3, B 3.0, etc. So students' letter grades for each assessment are converted into the equivalent GPA, a weighted average of relevant GPA for each assessment is computed, and the resulting GPA is converted back into the letter grade that appears on the official transcript. (The alternative would have been to calculated a weighted average of the numerical scores from each assessment and then choose ranges of numerical grades from this final weighted average to determine the final letter grades in the course).

Considering that the letter grades/GPA equivalents were determined solely on the basis of the numerical scores, I objected to this method of computing grades. I explained that the letter grades contained less information than the numerical grades since they represented ranges of performance. I further explained that as a result, a student who with a higher weighted numerical average score could end up with a worse grade than a student with a lower weighted numerical average score depending on where each student fell in the range for each assessment.

The professor and I had a stimulating discussion, but he ended up sticking with his original method of computing the final grades, i.e. calculating a weighted average based on the letter grades/GPA equivalents that reflect ranges of performance. He suggested there was a qualitative difference between letter grades based on the ranges he had chosen.

I spoke with the Associate Dean who agrees that the method of averaging at least raises the question of whether the grading method was reasonable. I am considering making a formal request that the grading method be reviewed, but am not sure whether to proceed. In my view, the issue is a very simple. By converting and then averaging rather than averaging and then converting, the professor is making a mathematical error like a rounding error and introducing uncertainty into the final grade.

I wonder whether I am right. I wonder whether the professor's comment about qualitative differences between the ranges carries weight.

I also wonder whether my argument is aided by the fact that the first assessment contained two questions each of which was "worth" 50%, each graded out of 9. Obviously a weighted numerical average weights them equally in calculating the final grade. But does a letter grade that is based on the ranges from the combined numerical score of the two questions?

In short I wonder whether this method of calculating the final grade is mathematically unsound. If so, I wonder if someone could help me explain why using correct mathematical terminology and also help me explain it to non-mathematicians.

Thank you!

• It sounds like he has normalized each assessment so it has the "correct" letter grade given the difficulty of that piece. That being case, averaging those letter grades makes sense, as they are commensurate. Meantime, raw scores are not commensurate. That sounds perfectly reasonable to me. – Simon S Jun 17 '15 at 19:05
• Different professors have different methods of putting together grades for tests, projects, quizzes, etc. to get the final course grade. As long as the method does not clearly violate something promised in the syllabus and is not discriminatory against irrelevant characteristics of students, they are entitled to their 'unique' methods. If you think professors are arbitrary in their assessments, wait till you get a paying job. A whole new world of irrationality awaits. – BruceET Jun 17 '15 at 22:33
• It would make no sense to average the raw grades. Why should an assignment marked out of 40 be worth more than an assignment out of 20 when they are both the same amount of work? I side with your professor here. – Patty Sep 29 '16 at 2:12