The way I see it, every child who is not either the youngest or the oldest is the/a middle child.

With 3, that's #2. With 4, that's #2 and #3. With 5, that's #2 and #3 and #4.

Though usually the context is that parents have 3 children because that's the most common version of having more than 2 children.

When I look at people who I know and their families, I can report that the middle child always appear to be self-centered, egocentric. As if they lacked love in their youth they're continuously trying to make up for the rest of their life. Oh, and they have twisted ways of justifying that behaviour.