Article Usage in Standard American English [duplicate]

"An average person" is a phrase with an article, adjective, and noun acting normally with each other. It means "any person who can be considered average."

"The average person," as the article "the" implies, is referring to a specific idea that is shared among all people (assuming that's possible) of what an average person must be like. In other words, it's referring to an archetype of the "default" person—the type of person any of us could be if we didn't have any eccentricities or distinguishing characteristics. "The average person" is a common phrase that, taken as a unit, has the described understood meaning.

All that said, the ideas expressed by both sentences are virtually identical.