Okay, this is a topic that goes under the heading "noun and verb agreement" (the old "spiel" of how countable and uncountable nouns goes with which form: plural or singular.
Well, this one is in the subset of special cases with said verbs - I mean plural or singular. So, an excerpt of a site goes with the following:
The following expressions
A number of, a couple of, a dozen of, a group of, the (a) majority, the (a) minority, a lot of, the rest of, most of, half of + plural noun/pronoun usually have plural verbs:
e.g. The majority of the people disagree with the new decision of the government.
There are a couple of children outside. A number of us are worried about it.
This brings us back to your case, if it was the majority of the American people (see? A "majority" is a group that we consider as an "are" verb -that is a "plural verb". So it takes a verb without an "s" with the third person singular.
The opposite with "news" that is singular with English agreement - "good news is good news (nenhuma notícia é por si só boa notícia).
Okay, now with the "average". In that case, it takes a singular verb
The average American works longer hours than the average German...