Plebeians and their letters

[Tertius Mummius]

You've said it yourself; the education level goes along with the money and time to spend on tutors and schools. There were no public schools.
On the other hand, children were given into custody of craftsmen at an early age to learn these crafts; this kind of "home schooling" must sometimes have included basic literacy and maths.
Compared to the medieval, however, literacy must have been astounding. We have of simple roof tiles, inscripted with jokes and comments by their slave makers, curses and prayers, price and adress tags, owner marks on simple items which indicate that reading and writing was not just the privilege of the ruling class.