What data about grades should I tell the class? Make public?
Revealing information about grades is normally directed by some combination of university policy and government regulations (if one is teaching at a public institution of higher learning). 

Where I teach, for instance, all grades for written exams are officially published, but semi-anonymized by replacing the students' names with their student ID numbers. In addition, the aggregate statistics are also published, along with the rubric for converting "raw" scores into final grades. 

My general belief, however, is that grades are an "internal" matter, that should not generally be publicized beyond the extent required by regulations. There is no need for everyone in the world to see the grade distribution.