I wanted the exam to sort out the stars, the average Joes and the duds, so it had to be hard and have a wide dispersion of scores. I succeeded in writing such an exam, but when the students got their results they were in an uproar. Their principal complaint was that the average score was only 72 points out of 100.
What was odd about this reaction was that I had already explained that the average numerical score on the exam had absolutely no effect on the distribution of letter grades. We employed a curve in which the average grade was a B+, and only a tiny number of students received grades below a C. I told the class this, but it had no effect on the students’ mood. They still hated my exam, and they were none too happy with me either. As a young professor worried about keeping my job, I wasn’t sure what to do.
Finally, an idea occurred to me. On the next exam, I raised the points available for a perfect score to 137. This exam turned out to be harder than the first. Students got only 70 percent of the answers right but the average numerical score was 96 points. The students were delighted!
I chose 137 as a maximum score for two reasons. First, it produced an average well into the 90s, and some students scored above 100, generating a reaction approaching ecstasy. Second, because dividing by 137 is not easy to do in your head, I figured that most students wouldn’t convert their scores into percentages.