"the average person" vs "an average person"

Solution 1:

... the average X... conveys the sense of some abstraction representing a category, and allows you to treat that abstraction as if it were a person. Think of those pictures where many faces are "averaged" to produce some kind of composite, but generalized to non-physical (or not only physical) attributes.

That is, the average Canadian doesn't refer to any specific Canadian, but personifies some combination of traits thought distinctive (in kind or degree) of Canadians in general. For reference see the mythic man on the Clapham omnibus (or here, etc.).

Now, an average Canadian would be any specific Canadian who, being selected, is subsequently judged to be average according to some criteria.

So, the former discusses some abstract set of attributes, only metaphorically personifying them into the average Canadian.

The second chooses a concrete Canadian to stand as the examplar of these attributes.

Solution 2:

They are both correct, but only "the average" seems to be the most common one. Since there's only one average in this context that talks about the whole nation, it doesn't matter if you prefix it with "the" or "an". But sticking to the more idiomatic one would be a better choice, which is "the average."