The "turn off wifi" suggestion was simply another way to try to narrow down your draining battery issue, which I take it is the remaining problem for you...
So then, if you go into Settings | Mobile Data and then Menu, then select "Show WiFi", now when you go into the Settings | Mobile Data, you will see two tabs, one for Cellular Data, and one for WiFi data. Scrolling down on either of those tabs will show the heavy consumers of data.
Are you synching your email often? Are you backing up to the cloud? Are you running some other social media program that is consuming CPU cycles and radio bandwidth?
It takes energy (Battery) to communicate via WiFi. That doesn't make your phone a sipper of power. See if anything stands out.
That battery graph was next to useless for diagnosing problems. Just try what I've suggested.
And yes, I KNOW you need to use WiFi. I'm trying to help you determine if there is one program that is utilizing your WiFi connection a lot that may be the source of poor battery longevity.