I have everything turned off on my phone (wifi, bluetooth, gps, sync, play store updates only while on wifi, etc.) and use power save mode and get terrible battery life when not on my wifi. I always have 4 out of 5 bars for signal so it could be that it is sort of weak and using more battery to get a better connection but on my Galaxy S 1 I had a slightly worse signal and the battery life didn't drain this much. The only thing using my battery is cell standby (64%).
I'm at work now and since unplugging from the charger at 100% after 3 hours and 16 minutes I'm down to 83%.
Unless your phone is defective, it'd suggest you may have installed some program or widget that is draining battery on idle. For example, I was trying out Go Power Master which tracks power consumption and other things. My phone's battery was losing power 3-4x quicker, especially when it is actively used.
My phone has been idling most of the time and currently is at 1d 2h and the battery is at 51%. And my signal at office isn't very good.