I am facing an issue to compare dynamic data. The situation is something like this as described below.
Suppose I have $n$ students in a class and I take an exam that was very tough and since the students got very low grades so I used z-score normalization and gave the students their scores. Now after that a new student comes and wants to give the same test, now if I try to give the new student a score using z-score then the score of the new student will change the mean and sd and then I will have to rewrite the score for all the previous n students which I can't. So how shall I score the new students?
I have tried to think of the solution using normalization but I see no solution for such dynamic data. I came up with this while I was recently trying to analyze some dynamic stock market data. My main motive was to normalize the data so that I can compare it with other data. The min-max normalization also does not work since the max and min can change with the new incoming data. Any help will be truly appreciated.