Word or phrase that describes the biased perception of a group
Solution 1:
I believe the word you're looking for is stereotype. Stereotypes may be treated as a representation of the "typical" group member, but in reality they are most often a characterization of the stand-out traits of "highly visible" members. These members might be known as extremists, depending on the type of group (e.g., religious extremists). They also might be known as geeks (e.g., science geeks).