Finding the minimum and maximum sums
Instead of calculating two sums, you could just calculate one: the sum of all elements. Then, the min sum is the sum minus the maximum element, and max sum is the sum minus the minimum element.
Note that sorting just to find the minimum and maximum elements is inefficient, because sorting is generally an \$O(n \log n)\$ operation,
and finding the minimum and maximum (and the sum) is possible in a single pass, which would be \$O(n)\$.

Hard-coding the number 4 makes the solution very rigid, applicable to only this specific problem. In your implementation you could use the length of the array instead in a way to make that number 4 unnecessary, and easily make your implementation applicable to a more general set of problems. The number 4 is an artificial restriction; it's wise to get rid of it.