For me, it's also dependent on mood...or maybe more that I'm not quite either, so my mood changes my perspective on which I'd call myself. Introverted days are when I just find myself tuning out and becoming quickly tired and impatient with conversation...I just want to be left alone to get my work done or to get home and quietly relax. But, then when I'm feeling extroverted, I'll be the one stopping into visit people and I actually feel energized by being around groups of people. The reason I'd really say I'm probably a little in between the two is that most of the time I am happiest to be doing stuff in small groups. Unless I'm just trying to focus on getting something done without any distractions, I usually thrive when there are one or two people to chat with at a time, or no more than a group of about 5 or 6 to work with as a team. If I'm completely isolated from people, I crave more interaction, but if I go to a party with a lot of people, I also start to feel overwhelmed and exhausted by the whole thing. I can go around introducing myself to people and having conversations, but it's something that requires effort and I'd rather just sit in a corner with a small group and just talk with them.
Overall, my view is that being introverted or extroverted isn't an either/or thing, but like many other things, is more of a continuum from one extreme to another. Some people are so introverted as to feel uncomfortable with any social interaction. Others are so extraverted that they can spend a night with a large group of total strangers and know every one of them and have invitations for further social gatherings with them before the evening is out. I think most people fall somewhere in between.
I wonder if an easy way to tell whether someone is an introvert or extrovert is what sort of parties they hold? I would think a very introverted person would not really be interested in parties, but would instead just choose to invite over one or two friends at a time, or maybe just sits around waiting for someone else to issue invitations. A very extroverted person might go around inviting huge crowds to a party...the types of parties that fill the house and spill into the backyard. And, someone in between might be more likely to have a small group over for dinner, or a more tame party with under a dozen people invited.
So, I guess the question I'd be more likely to ask wouldn't be "Are you introverted or extroverted?" But, instead, "How introverted or extroverted are you?"