Did you read the description?
going(8) -> 1.1466517857142857 which truncated gives 1.146651.

but n is odd now. not even.

Obviously, if n is odd, the middle term is the one at the center.

EDIT:
n means the length of string sequence(all strings formed by rearranging the letters in s, and ordering these strings in dictionary order), not the length of string s.

What happens if I pass an empty list of names? What happens if I pass 0 as the umpteenth cola?

Why are you asking this? There should be no tests with index = 0 or queue = [].