As some have said, labeling one as "normal" or not is rather detrimental to the society in a whole, ostracizing those who are different. However, since you based this thread off of one you saw, I will not point fingers.
Anyhow, I tend to be extremely introverted by myself, with much self reflection, almost to a religious or philosophical extent. I also tend to be very artistic, and my true emotions are shown when writing stories as my introverted self, many of which have quite a bit of symbolic violence and emotion, which I actually feel as I write the story down, whether it be in word or image form.
When in a group, I tend to be at the other extreme, although this quality has been drifting from me for some time. I tend to be rather loud and aggressive, and lacking of deep thought or irrational. I tend to be more affected by constant battering in this state than in my introverted self, and I tend to overreact.
All in all, it's up to the reader of this post to decide whether these characteristics are "normal" or not.