Is "Overall, students buy their lunch from the cafeteria." a grammatically correct sentence?

The first sentence is clumsy and arguably wrong. Replace the word "overall" with "mostly" and you've nailed it! 

The first one doesn't make much sense to me 

That's what I thought, but I just want to verify before I add it to my list of errors in our Yearbook.

Mathematician, you don't really need the word "overall," anyway.

"Most students buy their lunch from the cafeteria."  

"Most" implies "overall."

"Overall" is superfluous language.

 P.S.......that's as much as I know about the English language........

My question is: does the first sentence work?

I like Chris's sugestion best.  "Overall" is meaningless.   It is worse than meaningless.  It is confusing.

And I still do not think that the first sentence makes sense.  

Hey, Mathematician.....if you really want the "definitive" answer to your question....send it to kitty<3......she's the real "English pro" on here.......if she doesn't know......no one does......