Automate Text Number Calculations

I have a plain text file filled with numbers separated by single spaces. I need a small, reliable script that will read that file, calculate the total sum, compute the average, and output the numbers in sorted order.

Here is exactly what I expect:
• The script reads one input file containing space-delimited numbers.
• It prints (or writes to a second file) the sum, the average, and the full list in ascending order.
• The solution should run with a single command on any standard machine; Python, Bash, or another lightweight option is fine as long as it needs no proprietary software.

Please comment the code clearly so I can tweak paths or formats later, and include brief usage instructions once everything is ready.