As mentioned, this is an often discussed issue in the Apple forums, which I spend time in since I own many Apple gadgets.
In the settings on the phones under Cellular data, is the option to "Use cellular data for:" and then a list of the Apps on the phone. turning off most of these switches, especially for games, Apps store, You Tube and many others that use the screen.
You can also look in settings under mobile data to see what is using the most data. (Facebook, whatever)
The phone will still default to mobile data in sleep mode if not plugged in to power, but will not use large amounts of data.
Only the Apple iPhone does this. (Love my android!)
It is easily controlled by changing the settings under Cellular data.