Unusually high data usage by Android os?

Google Backup is one major culprit - turn that off.

Otherwise, check running apps and see what's doing the data transfers.

No, 1 GB is not common for background traffic unless you actually download something. Did you download apps or something? Watch videos? Synced your files from another device or the cloud? Must be something.

On your device, go to Google Play, find the settings WITHIN the app, and make sure it is set to Only Update Apps Over Wi-Fi

Now it should never update apps over cell data unless you manually tell it to.

I also keep both cell data and Wi-Fi off except when I need them, and I only turn on one or the other. I turn off GPS and set Location setting to the lowest offered (may be Off or Battery Saving).

My personal choice is I turn off every Google feature that would use bandwidth - I turn off Sync, Backup, Gmail Sync, etc. I don't need to get my mail on my phone (of course you need to not mind losing everything if something goes wrong with your phone). If I do need to send or read mail then I need to use the browser and go to gmail.com (Gmail app won't work with Gmail sync turned off).

I also don't install piggy social networking apps. I don't want somebody else's stupid Facebook etc posts eating up MY cell data. I do use a Twitter app but it seems to not download messages unless I open it.

I get OVER A WEEK of standby on one battery charge. I'm a light phone user - couple of calls and a few texts per week, maybe play a game at lunch, view/take/show a few photos. When I charge the phone every Monday I often have over 50% battery remaining. I occasionally use cell data at a restaurant (if they don't have Wi-Fi). I have no need for cell data to be on all the time.