I almost always feel like I'm representing a group – if not more than one group. When we lived in Alaska, I represented Caucasians. When we lived in Spain, I represented all Americans. When I go to software conferences, I represent all women. When I go to software conferences in Europe, I represent women and Americans. Talk about pressure to do a good job! It's probably not true that I'm always representing all those groups, but I really feel the responsibility to do a good job for everyone I represent, not just myself.
I have a friend who turned down a promotion to management partially because she realized that all women were being promoted out of technical positions and she was worried there would be no technical female role models left. (Which as a manager who'd been promoted out of a technical position, immediately made me feel guilty!)
It's good to know I'm not alone in feeling that I represent my cohorts. For my part, I'm going to try to think of people more as individuals and less as representatives of their various groups.