Humorous answer: the average user is a mythical being who always agrees 100% with all of the opinions of the co-worker currently imagining this instance of the average user. As such, he is a weapon wielded with great ferocity in design meetings.
Real answer: as many have pointed out, there is no such thing, or at the very least it is context-dependent. The real question is whether there is a better term. I would say that there is no generic term - there are many different types of personas, and all personas must derive from business goals.
The list of possible business goals is endless, and the list of persona types is equally endless. Probably the simplest and most enduring is translating the business goal of "grow" into an average user we call the "prospect". A business intending to acquire new customers must make an effort to understand the characteristics of non-customers and whether there is a group of them who have needs that the business could feasibly meet. They could be grouped on needs, attitudes, financial situation, geography, type of household, a million other attributes, but once having identified a relevant group, it's necessary to flesh out the picture to understand how to solve those needs.
For example, a brand-new pizza parlor would probably define a few common factors for its prospects - people who eat out or order food; people who live in a certain area; people who haven't heard of the brand-new pizza parlor. From there, the owner might sift through Yelp reviews, knock on a few doors, or stand out in a shopping center to ask people a few questions in exchange for a coupon, and the characteristics they learn about will hopefully tell them something about how they can make sure people find out about them, and what they look for in a place to eat. Now he knows his average user.