How do I extract stats about a given test item in the gradebook - e.g., high/low scores, median, &c?
Check out this answer and see if it helps:
How Do I View the Mean/Average Grade for an Assignment as an Instructor?
I don't think there is a way to "extract" them out of Canvas, but you can view all the information you are looking for by going to the course analytics page and hovering over each assignment.
How do I view Course Analytics?
Retrieving data ...