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?
Best Answer
I assume that when you say "The aggregate average of everyone else's scores is, say, 92%" you mean "The aggregate average of everyone's score including you is 92%", but that does not really change anything.
What you cannot say.
Consider two situations: one is that someone else got 89% on the test, you -- 95%, and all others -- 92%. Then yours is the best. On the other hand, suppose there are 10 people taking test. Someone else got 25%, you -- 95%, and everyone else -- 100%. Then the average is still 92%, but now you are the second to the last. So, you cannot really deduce your rank.
What you can say.
One thing you know is that, according to the Pigeonhole principle, there is someone who got less than 92%, because there is someone (namely, you) who got more than 92%, and 92% is the average score. So, your score is not the worst. :) But, as I have shown you, it can easily be the second to the last.
You can say more, if you know some other statistics (even without knowing the actual distribution). For example, suppose you know that the minimum score was 90%. Then you know that for every 2 scores above yours there must be at least 3 scores below you. This means that you are in the first 40% roughly.