Cinemetrics
/The art of statistics reveals fascinating things about the art of cinema. Seriously, these number crunching cinephiles do amazing things to track the changes of the art form. The best resource, IMHO, is Cinemetrics. Check out the site to see info on shot duration averages for individual films and for the industry as well.
People tend to theorize that shot duration is shrinking as the medium changes over time. That's true, but the details of how and when those changes take place are interesting. For example, some believe that shots shortened up with the early advent of VFX. This was, apparently, due to the poor quality of the effects to the filmmakers would not want to linger on imperfect elements. This only applies to effects films, so you can see that the theory doesn't or shouldn't hold for all movies of that period.
The site provides a ton of data, and great instructions on how to interpret it from acronyms to graphs and more. You can also conduct your own analyses by using the site's free software and following instructions provided.
Finally, don't miss the Measurement Theory page. It provides an impressive list of scholarly works that take statistical analysis into account within film analysis.