I have a database of 10-star movie ratings (similar to IMDB). For each movie the raw data is a distribution of votes from 0-star all the way to 10-star, and I have also computed the mean and standard deviation of the votes for each movie.
Now consider the set of all the computed standard deviations. Is there a known statistical distribution that this set is expected to follow in the general case? And if so, how do I compute its parameters?
Addendum: We cannot assume anything (namely normality) about the distribution of the movie scores themselves.