Jeni's Musings

English grammar, unlike other languages, is more descriptive than prescriptive. I.e.: Anything goes, even stuff by Shakespeare!

The sentence that you quote sounds to me plain wrong.

Any of the following IMHO is better:

“Typically students in the program take about six years to complete their course”

“The typical student in the program takes about six years to complete the course”

“The typical student in the program takes about six years to complete her course” (or his course).

You might like to read “Bugs in Writing” by Lyn Dupre. The book gives examples of phrases that, although strictly grammatically incorrect, are clear and should therefore be used and of phrases that, although grammatically correct, are not clear, or in some way awkward, and should therefore be avoided.