Are course grade distributions supposed to be bell shaped?

The distribution doesn't have to be of bell-shape. In very large scale open exams it may be reasonable to assume a bell curve. In many other situations, the distributions can be affected by the class size, mix of the students, objectives of the course, validity of the exam questions, and difficulty of the exam questions, etc.

Class size: The smaller the class, the harder to observe any discernible distributions, such as a bell-shape normal distribution.

Mix of students: If you're teaching a quantitative class and there are two streams of students from i) art programs and ii) engineer programs, you may see some other distribution like a double bell-shape bimodal distribution.

Objectives of the course: Some courses can be designed based on a fixed and stringent set of standards. For instance, if you teach anesthesiology and the passing grade for the students to take the board exam is 90%, the end distribution is unlikely to be bell-shape.

Validity and difficulty of the exam: Invalid questions may lower the accuracy which prohibits you to see the true distribution; overly easy or hard exam can move the curve towards high- and low-boundary, causing truncated bell-shape distributions.

If I have to give an assessment I'd first suggest removing the 0% as it's a special case and yet tilting the impression of the curve quite badly. For the rest, I'd say if you're teaching an introductory course in which students are expected to gain a good foundation, this is not a bad distribution. If you're teaching a very advanced course, with nearly 20% getting close to full mark then the assessment may benefit from a re-tuning.

Generally, I'd advise:

  • Analyze the grades and your course objectives in tandem. Just grade distribution itself does not tell if you're doing a good job.

  • Accumulate more data across cohorts of students. I find that after 3-4 times teaching the same course the patterns would start to emerge.

  • Compare to historic grade distribution (just a few years before you picked this course up) to make sure you are not way off. Consult the appropriate dean if they are.

  • If so inclined, try to analyze your exam items. There are special statistics to check if your exam questions are "good" questions. Most academic institutes should have an education affair office that can help you.


This looks to me like the sort of distribution you would expect from an exam that is simply too easy, and fails to distinguish at the top end.

You probably do have a roughly bell-shaped distribution of student abilities, but since in your exam the middle of the bell is at 85% or so, all of the high-ability tail inevitably get lumped together in the 95-100% bar.


Remember that your primary task is not to accurately tell better students from worse, but to make sure they learn what they are supposed to. This is also the role of the test: for students passing a test is supposed to be a fixed, specific goal to achieve, not a competition.

Therefore, the proper question here is: do you actually believe all of your students except for those unlucky few deserve passing your class? Do they learned what they were supposed to learn? If so, this is fine. The scores do reflect good on you that you taught your students well. This might also be a sign that it's not the test that requires adjustments, but the curriculum—you could probably teach more material in that class, and it will also indirectly lead to the exam being more difficult.

If not, then you should definitely adjust the test.

Some time ago I collected graphs from some documents from Polish Ministry of Education on the high-school exam. This is a huge sample (around 300k yearly), and you can see that scores do not always take a bell shape. Some useful discussion on interpretation of these graphs is in a reddit thread, especially explanation on the peak around 30% (the passing point) of the language exam.

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Grades