Here in this 1918 news advertisement we have "proof" that it wasn't uncommon for people (especially women) to be dishonest about their age. Even today, many people consider one's age to be privileged information! Others just weren't good at math or maybe they couldn't correctly recall what year someone was born. Census records can provide valuable clues about families and people, but unfortunately, they are not a reliable source for age or birth date or even birth place.
"How old is Ma? She won't tell the census man".
Bath Plaindealer 1916-1918
Bath, New York