2
$\begingroup$

Say you take a test and are told your individual score, as a percentage. Eg: 95%.

You are also told the aggregate score (average) of all students together, as well as how many students in total took the test. Eg: 92% average of 14 students. You are not allowed to know individual scores of any other students.

What algorithm could you apply to estimate your percentile ranking among students? Eg. You scored in the upper 10% of students. How can you use assumptions about distribution and deviation to calculate a realistic percentile ranking?

  • 3
    Without doing any assumption on the score distribution, is almost impossible to answer this question. The worst case is that 3/95 of the student has scored 0, and 92/95 of them $95+\epsilon$, in that case you are ranked in the worst 3/95. The best case is that everyone has scored 92 point, so you are the best one. Every percentile between 3/95 and 1 can be reached with the right distribution. You need to do some hypotesis on score distribution (eg. each student have the same probability p of know an answer, and there are 10 question. find p such the mean is 92, and find your percentile)2012-04-23

2 Answers 2