When we choose median as pivot , this means after applying partition the division into 2 subarrays is predefined that it will get divided into 2 halves..So recurrence relation for time will be :
T(n) = 2T(n/2) + O(n) [ O(n) time is required for partition algorithm ]
==> T(n) = θ(nlogn) [ i.e. as division into subarrays is prespecified so worst case = best case = average case ]
Hence θ(nlogn) is the correct answer for the given scenario..
If however , we say central element is chosen as pivot..So it may go either at first or last or middle of array..So times will differ in that case and hence worst case will be O(n2)..