Average between n numbers Is it possible to calculate the average between n numbers in a static random access array of some size in less than $O(n)$ time?
I know that the trivial approach is $O(n)$, but can I do it in less time using a data structure or a certain preparation? or both?
I am asking for hints, not a solution.

Note: The array is of some length. What and I mean by between is when given 2 indexes a and b, I have to calculate the average of the sub array $[a+1,b-1]$. And I have to keep it updated while the data structure is managed, that's why I said it was a dynamic set, in other words a random access array. I do not know of any restrictions, just asking if it's possible in less than $O(n)$.
I'll assume that you are computing the average of the elements of an array of fixed size and that you can change the value at some position at any moment. You want a data structure that supports the following two operations:


Update element at location $i$,
Query sum of elements in range [$i$, $j$].


A binary indexed tree (aka Fenwick tree) performs both in $\cal O(\lg n)$.