I have had Samsung galaxy S3 for almost 2 years, no battery problems. Try this: From the main screen go to settings, scroll down to Battery and select it, you should see all of the running applications and their power usage.
Mine has:
Android system 19%
Device Idle 17%
Android OS 16%
Cell Standby 14%
Screen 13%
Xfinity Wifi 4%
AccuWeather 4%
Google services 3%
com.andriod.systemui 3%
My phone battery easily lasts 1 full day (to typically 65%) and can go a second day.
I have battery power saving mode ON, and I use the automatic screen background on Auto as I was advised that both of these make a big difference in battery life.
My wife's phone battery life was getting so bad that I purchased a new battery, for less than $10, and that seems to have helped considerably.
Hope this helps.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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