I think it depends on each person's ability, sort of like how in the real world students may graduate a year or more before or after their peers based on their test scores.

That was true for Itachi, when he graduated as a Freshman. But I'm talking about when he or the average kid would start studying at the academy.

I want to say between four and six. Four because Kakashi was said to have graduated from the academy at five and six because Itachi graduated at seven.