Consider these two sentences:
A Scranton family has an average of 2.1 children.
The average Scranton family has 2.1 children.
I've seen both used. The first one seems reasonable, but the second one seems wrong because you're applying average to family, not to numbers.
To me, saying "the Jones are an average family" seems legitimate, but if the Jones have 2.1 children, they're anything but average.
Is the second sentence grammatically correct? Is it understood to mean the same as the first sentence?
Inspired by the question, Meaning of the expression "2.1 kids".