Chances are, the data consumption is the iPhone performing background Administrative tasks. Another option could be apps running in the background. If you pull up your Verizon Wireless account online, there should be a tool that gives a general breakdown of data usage. iPhones also provide a breakdown, but, the user needs to reset the counters in order to get accurate readings.
I, myself have a 1Gig/month data allotment. I keep 4G/LTE disabled to utilize Wi-Fi when at home or in locations were it is available. I only activate 4G/LTE on an "as needed" basis. Most months, my data usage is, for all intents, 0.
Thanks, dexman, for the excellent explanation of how data works. Xavair6, I understand how you feel, and data is expensive so the advice already given was a great recommendation. Although you are connected to WiFi, your device is still using data for your apps running in the background, and sometimes you can even lose the WiFi signal temporarily and be unaware, because the data will take over quite seamlessly. The best way to prevent data usage is to keep your data turned off whenever connected to WiFi. I have three devices on a 2GB plan and use less than 1GB. Here is a link that has different options to monitor data usage: http://spr.ly/6604EVvFr.
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Data reporting to your online account is not done in real time. The actual data use could have been hours earlier.
Towers note when a connection to a particular IMEI/ESN (International Mobile Equipment Identity/Electornic Serial Number - unique to your phone and SIM card) opens, pass to a new tower and closes. Once it closes, it sends data totals back.
The connection closes when you leave a tower's area, connect to wifi, turn an app off, turn off your phone. Think of each tower like a faucet with a measuring cup with your phones IMEI number on it. It notes when you connect, when you pass on to another tower and disconnect because you are connected to wifi, turned apps off, or turned the phone off. It is then that each tower can measure and starts sending back totals. This is of course when you are home, on wifi, phone off and asleep.
a SIGNIFICANT issue with iPhones as they age is the Wifi antenna fails. If you remove the SIM card and try to connect to internet sites with Wifi onky, and cannot, you have a faulty antenna.