What are considered as appropriate mean/median grades for college-level calculus and linear algebra in United States (out of 100 or out of 4.0)? [closed]

Question

What are considered appropriate mean/median grades for college-level calculus and linear algebra classes in United States (say out of 100 or out of 4.0)?

Please don't just say "it is different with different universities and colleges". Can anyone give me any specific examples where only a particular range of mean/median grade is allowed (or considered reasonable) in some U.S. university?

I am asking about this from the view of instructors/professors. I am not asking what kind of grade is considered "appropriate" as an undergraduate student. This question also aims at giving instructors an idea how to write exams and how to "curve" the scores in case the exams get too hard.

Answer 1

Hmmm. It's different with different universities and colleges. What can I say? It is also meaningless except with that university or college. And unusual system may need translation for external use, however.

A typical (not universal) grade scheme is 90, 80, 70, 60 for the minimum marks for A, B, C, and D respectively. However, grading is itself individualized so the grades often are awarded to meet those breaks. How well has the student mastered this material. "Near perfect" = 90-something. "Almost" yields 80 or so. Etc.

And numeric grades within a course are usually fractional. 3.8 is not as good as 4.1, but only by a little. For the transcript, though, they might be integers only or "half" scores: 3.5, sometimes with a max of 4.5. The overall will be a fractional GPA: 3.7 or 3.72, say.

Note that the grade distribution for a class is likely to be different for entry level (first year) courses and for later (upper division) ones. The less serious students have likely gone elsewhere. If the same "curve" applies then it is almost certainly unfair. A lower mean and a larger variance is likely for an entry level course, especially if it has many students.

I've taught courses at a top university where nearly every student earned and deserved 90 plus. They worked hard and made me work hard as well. I've also taught courses where students had been accustomed to be a bit lazy and were a bit shocked with their low grades. It was, fortunately, a convincing goad to get them to work harder.

Every group is different, not just every university. A group of 400 or so students might have something like a normal distribution of grades (honestly and fairly) but a group of 40 isn't likely to. It is too small. Probably skewed one way or the other as in the two examples above.

Note that large groups with many sections and lots of TAs need to take some precautions to assure that grades are fair across sections and TAs.

My advice is to make grading individualized but using a rubric. Consider every student to be different from every other with their own strengths and weaknesses.

And if you impose a grading scheme such that some student has to get low marks so that others can get higher marks (competitive grading) then IMO you are being unethical.

Your job is to teach them. I.e. set up the conditions for learning. It isn't primarily to grade them. You aren't the Hogwarts sorting hat.

At the end of a course, do an informal evaluation of your grades prior to filling out grading forms. You probably have a general impression about how they did "overall". If your grade distribution matches that general sense, then you probably got it about right. I had the luxury of being able to adjust grades upwards (for all) if I felt the individual grades were too low for what I saw as the learning. Never downwards, though. Surprises for students should be happy ones. This ability to adjust depends on some experience, of course.

See this post about imposed curves.

Answer 2

There are few cases where this information would be useful -- it varies widely from school to school. The only case that I can think of where you would want this is if you are a faculty member at a school where there is a political fight about what the grade distribution should be, and you would like to introduce data of the form "at U Michigan, the median grade is a B" into the discussion.

That said, I know where to look up this data at UMich, so here it is: The grade distribution for Math 115, our largest calculus course:

Unfortunately, this data is behind a log in screen (see here), but there aren't any FERPA issues with large statistical reports like this.

I would like to editorialize on people's sad inclination to put passwords on things. At Harvard, this information was collected in the CUE guide, which was sold in campus bookstores where anyone could walk in and buy it without ID. Now it is online, which make perfect sense -- but you need Harvard log in credentials to read it. Why??!!

Answer 3

I will assume you are referring to the distribution of letter grades, and that your university does not have a mandatory mapping from "points" to letter grades.

There are two different philosophies here:

• One is that the course should challenge the average student. So an average student should get a B (or somewhere between a C+ and a B+), with most of the rest getting As or Cs. If the average course grade is much higher or lower than this, then it's probably the case that the course was too hard or too easy, relative to the college's admissions requirements.
• The other is that course grades should honestly assess a student's familiarity with the material. Even at an "easy" college, students who get an A in calculus 1 should be able to reliably take a derivative and tell you what it means. If this means that you give very few As, that's just the way it goes; better that they fail your class rather than moving on to physics classes where they have no chance of succeeding.

Of course, in both cases, it's "theoretically possible" that all students will exceed all reasonable expectations and thus they'll all deserve As....but this is statistically very unlikely.

In the US, my experience is that the first philosophy is much more common. For most (STEM) courses, I would expect average grades somewhere between 2.7 and 3.3 out of 4. But you asked about calculus courses specifically, which may be one of the rare cases where the second philosophy is not so unusual, and a relatively large number of failures is expected. Of course, this will vary by school: MIT undergraduates will probably not struggle too much with calculus. But in general, I would not not be so concerned if the mean Calculus I grade was even lower than 2.7.