We have m datasets of n elements, where each element represents the grade of a student (from 1 to 10) for a given test. We are told that student Peter always achieves a test score that is the median of the class' results for a given test; if we would form a new dataset of the summed test scores for each student in the class, can we argue that Peter's summed score will again be the median of this dataset?
My intuition says we can, but I have a hard time materializing this into a concrete proof or argument. It would seem strange to me that the sum of each median would not be the median of this summed dataset (but this is obviously not a proof).