For sorted array, this can be done in O(log n)
That element must be a middle element.
And to make sure that middle element occurs n/2 times, first find the first occurence of this element(using binary search) which can be done in O(log N).
Now check the N/2+ first occurence index
if it is same as the middle element, then it is occuring more than N/2 times, else no other element has that much frequency in the array