The worst case time complexity of a typical implementation of Quick Sort is $O(n^{2})$. The worst case occurs when the picked pivot is always an extreme (smallest or largest) element. This happens when input array is sorted or reverse sorted and either first or last element is picked as pivot.
Although randomized Quick Sort works well even when the array is sorted, there is still possibility that the randomly picked element is always an extreme.
Can the worst case be reduced to $O(nLog_{2}n)$?
The answer is yes, we can achieve $O(nLog_{2}n)$ worst case. The idea is based on the fact that the median element of an unsorted array can be found in linear time. So we find the median first, then partition the array around the median element.
Running time of Quick sort algorithm depends heavily on the selection of Pivot Element