Share your experience!
3G will drain faster than 2G,especially if network signal is bad.
You should check if the same occurs in safe mode:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008
I wonder if the battery has been damaged.
You should get in contact with your xperia care:
http://www.sonymobile.com/global-en/support/contact-us/
No,it is not normal.But beside data,were any other apps on?