# Interpretation of Multiple Choice Tests

I’m taking multiple choice exams where I’m doing worse than I would like to be doing (6-7 out of 10). The question I’m trying to answer is if my score reflects an insufficient knowledge of the course or if the class average deems that the course was not taught or assessed correctly.

For a standard multiple choice exam, an uninformed class will score ~25%. For every percentage that the class knows, the test should reflect a certain grade. It is not true that a class average of 25% in a multiple choice implies that the class on average only knows 25% of the material. So to illustrate, we’ll use the minimum grade that is acceptable: 50%. If a student knows 50% of the content of the course, they should get what grade? Naively, we would think they would get 50%. This is false.

If a student knows 50% of the content, they will correctly answer 50% of the questions plus 25% of the remaining questions due to randomness. That means that their expected score is 50% + 50% * 0.25 = 62.5%.

Now what is the % of content the teacher would want their students to know? If I taught concepts, I would want 100% in the application based questions, but based on the curve of forgetting plus the expected amount of out of class studying, we can target a % of 80%,

Therefore, my conclusions are as follows:

- Scores or averages less than 85% should be investigated
- If I ran a university, I would not allow curving of grades, but at the same time, I would investigate courses that have averages less than 80%. It’s always possible for a class to be stupid, but if all classes are stupid, then something else is wrong.

- A flashcard system with filters and tags for the course is very beneficial
- Research into how to teach all students effectively rather than telling students what to do and hoping for the best