Please do :)

Thanks. This is an interesting option.

It is a good thing to stretch one's brain. Hint: each student experiences the average class size of their class. When you count them up by class you end up with 350 as the total perspectives of average, divided by 30 students. I'm not sure that helps.

That 11.66666 average is closer to a measure of dispersion, but still an averege. The variance is the average of the distance to the mean (the natural value of 10 in this case). In this calculation you have to account for every student individually. And well, the variance isn't 11.666 but is related to it

From the teacher perspective: What class size can I expect? 10. Only one teacher in each room, they are equally likely to be the teacher in each of the 3 rooms, so they can expect a class size of 10 on average. From the student perspective: What class size can I expect? 11.666 They are more likely to be in a large class; by definition only a few get the small. So, using this weighted average (class size x number that experience it) makes sense from the student perspective.

@@kirsteneilertson2478 that is a very asymmetric way of looking at it. Students expected values are according to themselves, but theachers' are also according to students, somehow!? To be more clear, your proposed reasoning has students being shuffled and averaging themselves, but teachers are shuffled among themselves, but then averaged on students. If you also average teachers on themselves, you get an average of 1 wich, compared to the "intuitive" average of 1 teacher per class will tell you that the dispersion on the teacher distribution is low, unlike the students' Like I said before, the 11.6666 average is more useful as a measure of dispersion. To better evidence my claim, standard deviation is defined as the square root of the difference between the 2 "kinds" of averages