You can definitely do this without sorting.

QuickSelect is average case n, and is, roughly, quick sort where you throw away one of the sides each time and recurse on the other. This has a fat tail for cases where you pick a bad pivot (similar to quicksort), but you can median-of-medians your way out of that problem if someone cares. (Median of medians being where you subdivide the array into, say, 5 arrays, recursively compute the median on those, and pick the middle median as your pivot, which guarantees linear progress per iteration)