How much bandwidth does just being connected to Xbox Live (on an Xbox 360) use per hour?

We have only 10 Gigabytes a month, mainly it is just me that uses it, my Mom may or may not use it at all (just for work sometimes). Every month we go over. I know playing online uses some, some games more or less than others, but I only want to know how much data just being connected and on Xbox Live uses an hour - no parties with mics, no multiplayer games - nothing. I know there is videos that are advertisements that are constantly loading on the homescreen, that alone must use a lot right? Someone please give me a best answer.