What is the word to mean to apply attributes of an entire race to a single individual?

Solution 1:

Where racism is a move from specific to general, discrimination is a move from the more general to the more specific.

discrimination 3. Treatment or consideration based on class or category rather than individual merit; partiality or prejudice

This means that prejudices held by an individual towards a group are transferred onto a single individual without regards to his individual merits. Of course, discrimination has a more general sense (as does racism) but according to your dichotomy, it fits the movement from general prejudice to individual prejudice.

Solution 2:

You are looking for:

stereotype : 4. (Sociology) A set of inaccurate, simplistic generalizations about a group that allows others to categorize them and treat them accordingly

In your case it would be racial stereotyping.