I have a list of random numbers with unknown distribution. This list is divided in N chunks with equal length. Then I have the average of every chunk, and the average of these averages.
Is it possible to derive the difference (min,max) between the average of the averages of these chucks and the average of the whole list, in case of unknown distribution?
Edit: I've missed the most important part - it is about integer arithmetics and therefore in this case the averaging introduces rounding.