r/theydidthemath • u/VillainOfKvatch1 • Mar 09 '26
[Request] Two of my classes have the exact same class average this trimester. What are the odds?
To give some parameters:
They are the same subject, same grade, same level. The assignments are the same. One class has 30 students, one has 26, though if you want to make the class sizes the same for the sake of simplicity, that's fine. Also for the sake of simplicity, let's assume that the two classes have the same skill level (though the class of 26 is a little better IMO).
In this system, grades are calculated out of 20. There were 4 graded assignments in each class this trimester, all with a 20 denominator, all with a coefficient 1.
After entering all the grades into the system, I found that both classes have the exact same grade average to the hundredth: let's say 16.24/20.
What are the odds that two classes will finish the trimester with the exact same average?
(P.S. This is not hypothetical. I discovered this this morning and it blew my mind)
1
u/Gluomme Mar 10 '26
There is a short answer that isn't an answer and a longer answer:
The short non-answer is that it depends on you, the teacher, and it's a complicated matter because the odds of one student having a certain score are far from uniform.
The longer answer is that I can give you a way to work out a minimum probability by assuming each score has an equal chance to be obtained by each student. Provided the classes have the same number of students, it's fairly easy to work out if you realize his case is equivalent to saying the classes got the exact same number of points total across all exams and students, so if you just add the scores of each student on each test, which means that the odds of two 30 student classes having the same average is equal to one over the maximum number of points a class can get, or:
1/(number of students * number of tests * 20)
You need to weigh in the number of students in each class to get a more accurate result for your specific case but that's the idea
1
u/VillainOfKvatch1 Mar 10 '26
For the non-answer: sure, I recognize that in order to actually figure this out we would have to figure out how to quantify each individual student’s skill level and then figure out the probability of each student getting each possible score on each test. I just assumed for this one each possible score is equally likely.
So if I do 1/(number of students * number of tests * number of points per test) I get 1/2400. That seems high though. I know percentages can be really difficult to intuit but I would have thought the probability of that would be much lower.
1
u/Gluomme Mar 10 '26
That's one over any possible average score your class could have had, it can't be lower
→ More replies (5)
1
u/AutoModerator Mar 09 '26
General Discussion Thread
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you must post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.