Improve our rating average algorithm and display

[Josh-Cena]

Following our discussion with Miki, the average ratings for many courses do not fairly represent the quality of the instructor/course. This is especially true for average instructor ratings, which tend to "stick" because for courses we only calculate average within the same instructor where possible. For examples of unfair instructor ratings:

• A junior instructor got a poor rating in their first/second semester of teaching but improved later; there's no reflection on this general trend
• Professors who also teach intro courses (service courses is a tradition in the math department) tend to have lower averages than those who only teach electives because of different audience backgrounds/expectations, etc.

I think there are several things we could do here:

1. We should weigh ratings by recency. Courses taught more then 2–3 years ago should be weighted drastically less in the average.
2. Miki pointed out that weighing average by enrollment (which we planned to do) actually puts intro course instructors at a disadvantage because those courses have more students and those students tend to be more unhappy.
3. We need to have explicit documentation on how these averages are computed.
4. If possible, whenever we show an average, we should show other statistics such as sample size, standard deviation, and maybe display a graph against time to better put the number into context.

[bearsyankees]

I also would add I think we should give the user a choice here in what data they are seeing, whether that be a toggle for weighted ratings or not, or a slider for how far back they want data to go, or other options

[Josh-Cena]

Sounds really, really advanced for most users, I guess...