Did a backup. Also did a sync. Or maybe the sync stopped when iTunes reported it couldn't find the app YardSale. Is the sync incomplete if messages like that come up or do messages like that come up after the sync is complete?
Okay I'm erasing now....
I may be a bit late to answer your question, but I had the same issue on my iPad Air 2 and my 6s. The "used storage" was much higher than the sum of all the listed apps. I connected my devices to my Mac and iTunes showed that a huge amount of storage was eaten up by "documents & data" (17GB on my 64GB iPad and 9GB on my 64GB iPhone).
When I see your screenshot it looks like you have the same problem.
My solution was:
-download many movies and apps to fill the storage up to <500MB available
-try to download a movie which can't fit onto your device
-the device will show you a message stating that there's no storage left
-now delete every previously downloaded movie
The "available storage" should now be much higher than before. My iPhone had 7GB more storage listed under "available storage". This method was previously possible with movie rentals, but it didn't work for me and I had to do it with my purchased movies. I don't know exactly how it works, but when you try to download the movie which size is much larger than the available storage, iOS seems to delete as much used storage of "documents & data" as possible. I hope this helps.