Individuals give their ages in a variety of records before 1900 in the United States.
How many times were they asked for “proof” or “evidence” of their age? And how many times were they simply asked?
If it seemed reasonable to the clerk or official, that’s probably what got written down.
That potential for variability (or outright lying) increases if there’s really no penalty for lying.
A forty-five year old giving a wrong age on a census by a few years is an entirely different scenario from an underage minor lying to get in the military or get married.
Just something to think about