In Time Squared, the sister ship which I cant remember the name of is said to have been lost with "over a thousand people", and I believe that is supposed to include families. It should be the same for Enterprise.
The ratio of crewmen is more uncertain. In The Offspring, they visit the kindergarten, and a rough guess would put the total amount of children at about 50. If both parents are on board, and one is a crewmember, that is a hundred civilians. Most likely there some who only bring with their spouses/girlsfriends/boyfriends/etc, so say 100 more there. And then an even rougher guess on about 200 civilians on top of that (Ten forward always seem to be full of them), and we have about 600 crewmen left. Which still seems like alot for a ship that doesn't look to need that many people to be run. Of course, there could be a lot of work done that the audience don't see, for example the science departments.