Agreed , as all the above built-in functions [ConvertAll(),Min,Max] are internally using loops. they are sugar coated functions for developer.

Below is my solution for uses 2 reasonable loops and print the result as expected. kindly suggest if we can improve further the below code.

    long min = 0;
    long max = 0;
    var isFirstloop = true;

    for (int i = 0; i < arr.Count; i++)
    {
        long tempCount = 0;
        for (int j = 0; j < arr.Count; j++)
        {
            if (i != j)
            {
                tempCount += arr[j];

            }
        }

        if (isFirstloop)
        {

            min = tempCount;
            max = tempCount;
            isFirstloop = false;
        }
        else
        {               
            if (tempCount < min)
            {
                min = tempCount;

            }
            else if (tempCount > max)
            {
                max = tempCount;
            }
        }
    }

    Console.WriteLine($"{min} {max}");
    Console.ReadKey();