There is no "average person"

"The average American uses..."
"Average LA residents drove..."
"The average family has 2.4 kids."

I've heard phrases like this too many times this week, and I have to put my contempt for them in writing. My wife knows how much I hate this phrase, and it's a running joke for her to point it out to me when we hear it.

Why do I hate this phrase? It's partly because it's not accurate. When someone says "The average American owns 1.6 cars" what they mean to say is "Americans own an average of 1.6 cars." Such phrasing has become notoriously ridiculous in such cases like cars and kid for which it's impossible to own half a car or have half a kid. But it sneaks in through other statistics that make more sense as fractions (e.g., "The average Californian uses 54.3 gallons of water a day").

I'm a stickler for grammar and accuracy, but that's not the main reason why I hate this phrasing. It goes deeper than that.

1) It makes interpretation of the statistic difficulty for a lay audience, and makes it easy to criticize the statistic (or statistics in general). "No one has 2.4 kids!" "Who are these 'average' people?!"

2) There is no "average American" (or any member of any population) but there can be a multivariate average of multiple characteristics (or the most frequently occurring characteristics) among Americans (or any other population). In this "The average person..." phrasing, we're not talking about that, though. If you think through the grammar of the sentence, it implies that they've created some sort of multivariate average from some sample and are reporting a statistic for that group. Really all they're doing is misapplying the term "average" to the people (e.g., Americans, Californians) when it should be applied to the outcome (e.g., cars, kids, gallons of water).

Understanding statistics in popular media is already hard enough, and many of them are easy enough to critique for many reasons. Why confuse the public more and paint a bigger bullseye for targets of criticism, when a simple grammatical fix would make things clearer?