Some examples I've seen played, in older versions of D&D, but that makes little difference to this:
Hoyou the Barbarian: Intelligence 3, Wisdom 17. He was horribly inarticulate, and could neither make nor follow plans, but he never did anything that was obviously stupid, either. He didn't really think, but he had superb instincts. I don't think we ever learned his real name, if he actually knew it, "Hoyou" was just a worn-down version of "Hey, you?"
Fay was a magic-user, and a knowledgeable one, with Intelligence 18, and, sadly, Wisdom 3. You could talk her into trying anything, since she had no judgement at all, and would fall for any vaguely plausible scheme.
"Hi, there, my name's Richard Head, but you can call me Dick!" He was a priest of a god of stupidity. He had about Intelligence 6-7, and Wisdom maybe 9. He was very articulate, even glib, but you soon learned that what he said made very little sense and wasn't worth paying attention to.
The Town Giant - a town giant is what you get when hill giants have been working as muscle and bouncers in a town for a few generations, and getting bashed on the head regularly. He was another follower of the god of stupidity. He didn't talk much, but you still had to keep an eye on him. He valued things strictly according to their direct usefulness to him, or the amount of beer you'd get if you offered them directly to a bartender. His escapades included using a Crystal Ball as a throwing rock, because it could hit monsters that you needed magic to harm (nobody was brave enough to take it from him, until a wizard used Charm Monster and swapped it for a +2 boulder), and eating a dead PC that he'd been told to carry back to town.
The point of these is that stats are only a starting point for forming a character's personality. The personality needs to be compatible with the stats, but that is the only restriction, and there's a lot of scope for interpreting the stats.