- Some students had an advance copy of the test
- The grade distribution indicates cheating
What the professor doesn't know:
- Who cheated
Unless the university has access to a students network traffic proving they had access to the test, there's no way to be sure who cheated. The fact that the professor trudges through threats and vagaries for a full 15 minutes only seems to underscore this.
I have in the past had wildly fluctuating grades. Don't believe everything your powerpoint-prettied software stats tell you.
This actually happened when I was studying engineering at Waterloo. The course was calculus 3 and the prof, who normally taught math majors, didn't know that there was a university commissioned exam bank with previous exams for courses. Course coverage was sporadic for all but final exams, so we normally didn't check it, but the previous midterm was actually there. One of us found it 24 hours before the midterm, so half of us got it and half of us didn't. The prof had reused the hardest question. Long story short, nobody got in trouble, but the prof made it so your top and bottom "midterm" (there were 5 of them before the final) could be optional dropped together or not at all.