The question you're not addressing is: "Of what use is race"?
Wasn't addressing that... just addressing your use of only height as a trait mainly.
Race is pretty useless for classification in Scientific terms its value is more geographical,historical,cultural and social.
Different races or populations are more prone to various disease like cystic fibrosis, Sickle cell anemia, cancer all the way to Obesity due to diet/lifestyle and/or genetics. Different races also respond differently to certain drugs. The differance are in frequency in the population and not specific only to the race... They are specifically related more to family than race.
Researcher looking for a cure to a disease that occurs in higher frequency in a population(race?) won't that info be useful in some way?
As a businessman knowing a race likes/dislikes would also be useful as I can target my product specifically or the majority of them to make the most profit.
As a leader of a country knowing more about each of the races living in my country will be extremely useful to maintain harmony.
etc.
Knowing someone's "race" tells you absolutely nothing about them.
It tells me geographically where his ancestors came from... Its like a geographical marker...