Hi runawayparent, and welcome to cruise-chat.com.
I agree with the previous posters that a lot depends on time of year. School vacation weeks, obviously, are going to have the greatest number of kids -- but it is also a time in which the lines (including NCL) ramp up their kids' programming. Of course, there may be kids younger than school age on board at other times of the year, and some parents do pull older kids out of school, but those numbers are down tremendously from what you'd see during a school break.
I know, as I am not just a parent of a middle-schooler, but am married to a teacher. School vacations are the only times we can vacation.
Longer cruises also tend to have fewer kids onboard. Which ship will you be on, and when (roughly, if you're not comfortable posting the exact date)?