Some people claim to be both introverted and extroverted but they’re full of shit! You’re one or you’re the other. Period. End of Story. It’s chemical - as in your brain chemicals. That means unless there’s a pill that rebalances your chemicals so you reach some neurochemical ambivert nirvana, you’re an innie or an outie.
You can certainly be a strong, medium, or low introvert or extrovert but just because you are an extrovert who likes downtime to read a book or an introvert who likes to party (like yours truly), doesn’t mean you’re some mutant offspring of both. I think when people say they’re both it’s because they are confusing introversion with shyness or extroversion with being a loud, party animal. One has little to do with the other. It's about how you prefer to face the world and how you draw, for lack of a better phrase, your psychic energy. Extroverts need people and activities outside of themselves to feel alive and energized and Introverts need alone time and solitary activity to feel the same.
I would class myself as a medium introvert. I like a party where there’s food, dancing, or some type of activity which does not center on small talk, but the people and the activities don't energize me in the way they would an extrovert. Simply put: no after party. I was at the party, it was fun, and now there’s that thing called sleep I need to attend to. I seriously don’t need to stay until the last person stumbles out.
I also don’t mind, if I’m rested and in the mood, chatting up a stranger or two. I like people just fine, contrary to what some think (sadly my extroverted significant other thought I was a complete misanthrope until I set him straight). I just don’t need to engage them 24/7. Talking and hanging out is not my raison d’être. If I did that all the time, when would I read, draw, write or enjoy the movies? Exactly.