In 5 of 7 Muslim-majority countries most people prefer that women just cover their hair, not necessarily their face. But in Turkey and Lebanon, 1 in 4 don't think any covering is necessary.
That's what a study conducted by the University of Michigan’s Institute for Social Research discovered. The Pew Research Center just published the study which you can read here. Thanks to @jenanmoussa for tweeting the link.
Here's another interesting graph from the Center. And Max Fisher has an article about it in the Washington Post here.