A preconceived idea is one you built before you had enough facts or experience — and then you walked in carrying it. The word almost always rides with idea, notion, or opinion. Teachers and scientists like it because it names a quiet kind of unfairness: you are not trying to be mean, but the picture in your head got there first, so new information has to fight it. Though actually, the word does not mean the idea is always wrong. It means it arrived too early. A doctor who has already decided “this is just a cold” may miss something more serious. It is a fairly formal adjective. In chat, people say “I already had it in my head that…”