I assume that you mean when the computer is turned OFF.
It depends on what you're monitoring, the router or an adapter within the PC.
You need to be clear about what you need and what your equipment is.
Thanks for replying. I mean either way, if computer is On or Off. Does the program also measure how much data is downloaded using router wireless? I'm a zxv10 w300 ZTE
The best way would be to run your own test.
While the PC is ON and monitoring the router, record the totals from the router, turn the PC OFF but leave the router connected to your ISP.
While the PC is OFF, use your other wireless device for awhile so that the router records that traffic, then stop using that device.
Turn the PC ON and check the totals from the router which should be larger due to the traffic of the other device.