Quicksort- how pivot-choosing strategies affect the overall Big-oh behavior of quicksort?

Question

I have came up with several strategies, but I am not entirely sure how they affect the overall behavior. I know the average case is O(NlogN), so I would assume that would be in

Answer 1

The best pivot is the one which can divide the array exactly in two halves. The median of the array is off course the best choice. I will suggest this approach :-
select some random indexes
calculate median of these elements
Use this as pivot element


From the O(n) median finding algorithm, I think 5 random indexes should be sufficient enough.