WrongBot:
But I should not make decisions about individual members of Group X based on the statistical trend associated with Group X [...]
Really? I don't think it's possible to function in any realistic human society without constantly making decisions about individuals based on the statistical trends associated with various groups to which they happen to belong (a.k.a. "statistical discrimination"). Acquiring perfectly detailed information about every individual you ever interact with is simply not possible given the basic constraints faced by humans.
Of course, certain forms of statistical discrimination are viewed as an immensely important moral issue nowadays, while others are seen simply as normal common sense. It's a fascinating question how and why exactly various forms of it happen (or fail) to acquire a deep moral dimension. But in any case, a blanket condemnation of all forms of statistical discrimination is an attitude incompatible with any realistic human way of life.
The "deep moral dimension" generally applies to group memberships that aren't (perceived to be) chosen: sex, gender, race, class, sexual orientation, religion to a lesser extent.
These are the kinds of "Group X" to which I was referring. Discriminating against someone because they majored in Drama in college or believe in homeopathy are not even remotely equivalent to racism, sexism, and the like.
A few examples (in approximately increasing order of controversy):
If you proceed anyway...