Is it possible to make a graph using an applet?

yes

Could you provide and example / tutorial? Please.

Too lazy to use Google on your own, huh?

Try http://www.google.com/search?tab=vw&...graphs+in+java

Not too lazy I already tried googling around and it requires some 3rd party application / jar file installing. I was after a simple built in library to assist me with it.

well, everything you need to create your own charting library is right there in the core class libraries.
But why go to the trouble (unless of course it's a homework assignment you want to trick us into doing for you) of doing that when there are perfectly good components available?

Hm I've just come out of my yearly placement and have been heavly involved in Java. Apparently its cleaner to use built in java rather than prebuilt libraries.

I guess the guy that told me is wrong and im an idiot for beleiving him

indeed he is.
In some highly specific situations you may want to avoid any reliance on third parties, but usually you want to write as little code yourself as possible.

Why reinvent the wheel? Why go through months or years of development and testing to get to the stage where those third parties (often highly experienced in their field) are already?

If you go that way, why rely on a programming language written by others?
Why rely on an operating system written by others?
You could even question the decision to use hardware created by others made out of raw materials mined by others with tools made by others...