How do professors interpret normally distributed midterm or final exam scores?

Question

I had recently taken a class where things are poorly taught and much of the studying was self study. This then turned the course into a function of time and workload, and the resulting midterm mark is normally or bell shape distributed with a center of 50.

Needless to say, people who had less workload earned higher scores, people who had more workload earned less scores. After the exam, no one felt that the exam was a good reflection of individual capabilities but it is uncertain if the professor had gotten the hint.

How do professors interpret this outcome? Specifically, are there actions taken to some how adjust this (because most courses have an average passing around a C or 70 instead of 50)?

Answer 1

Unless you have access to every student's score, you cannot know that the distribution is a normal distribution. It isn't clear that you do have access to the scores, but in a comment you say, "the 50 percent people were slightly less than the people who got 30-40 and 50-60 but not by much." You have described a bimodal distribution -- one with two humps at the ends and a dip in the middle. Your "slightly less" says the dip in the middle is a small one.

My own experience as a college teacher is that a bimodal distribution is a usual and expected result for a fair exam. At the "good" end, you find the people who either worked hard or found the material to be familiar. At the "bad" end, you find the people who did not work hard. That is exactly what you've described, although you equate "worked hard" with "had more time to work."

As far as interpreting the scores, you don't say whether the scores you mention are percentages, i.e. out of 100, or have some other base. If they're grades out of 100, then that is probably, but not certainly, a poor exam. (The other choice is that there's an entire class of poor students, and yes, that does happen.) If I, as a teacher, got a result like that, I'd use the grades as they were, but work much harder on the questions for the next exams.

Finally, you question whether the exam "was a good reflection of individual capabilities." That's not what en exam is supposed to measure. An exam is supposed to measure your knowledge of the course material. A very capable person who doesn't study can and should earn an unsatisfactory grade.

Answer 2

Here is how I normally assign grades in a class of 30-50 students, given a distribution of scores:

1. Declare the average to be either a B or B+, depending on how satisfied I am with the class's performance as a whole.

2. To find the A/B cutoff, look above the average for obvious clumps. If, say, the average is 75% and there are ten scores of 85% or higher, and no scores between 80 and 85, then the scores higher than 85 are the As.

3. There will not always be obvious clumps, and in that case I put the cutoff somewhere between the average and the maximum in a semi-arbitrary way. I may look back at some exams to see if particular students did what I consider A work.

4. Determine the B/C and C/D cutoffs, then pluses and minuses, using a similar process.

5. To distinguish Ds from Fs, I don't make a numerical cutoff. Fs are reserved for students who have not shown me that they're actually trying.

The benefit of this method is that if I accidentally make the exam too hard or too long, the students don't pay the price. But I always try to make my exams straightforward, with at most one challenging problem, because experience shows that asking students to regurgitate what I've told them already provides a good enough range of scores to separate students from each other. If I've done things right, the average is usually in the low 80s.

Now, your professor may or may not use a system like mine. He may simply enter the scores into the grade book and use rigid, pre-determined cutoffs, regardless of the class's performance. The only way to know is to ask him.

By the way, you've observed that the people who spent more time studying got higher scores, and this strikes me as completely fair. If the class could be aced without studying, it wouldn't be a very useful class.