Finding average of a sample with single piece of data

Question

Is there anyway possible to guesstimate/estimate the average of a sample if you know just one of the sameple and its position when all available samples are arranged ascendingly and total number of samples.

example: lets say a student has scored 14.5 out of 25 in an exam in a class test and his rank is 4th out of 80 students, so is there anyway i can make a good approximation of what the average of the test could be?

Answer 1

You would need to know something about the variance of the set. Even to guesstimate. Using your example, what if all the students got 14.5 out of 25? What if 4 students got 14.5 and the rest got 25/25? You can see how the average can wildly fluctuate between those 2 cases.

With 80 students taking a test, you may be able to get away with Cental Limit Theorem, but that's a stretch if you ask me.

EDIT: I guess based on worst/best case scenarios, you could get an upper/lower bound for the mean.

• Lower Bound: 3 people get 0, everyone else gets 14.5
• Upper Bound: 4 people get 14.5, rest get 25/25

So for your example the mean would be somewhere between 13.775 and 24.225, but I'm guessing you wanted something a bit more specific than that :p