Suppose I have a number N of independent ratings of a given item, where each rating is an integer between 1 and 7 (inclusive). For simplicity sake, let us assume the ratings are normally distributed, though the mean and stddev will be different for each item.
I'm looking for a single number which will reflect how much trust I should put into the currently calculated mean. As an example, if I have N=1000 where every single rating is of 4, this trust should be pretty close to 100%. If on the other hand I have only N=2 where one rating is 1 and the other is 7, my trust that the mean is 4 should be very low.
I realise that a compute-trust function such as the one I've described above will likely need further parameterisation beyond the set of ratings. If you prefer, I can reformulate compute-trust in terms of "with 95% confidence, what is the probability that the population mean will be found within a given interval around the sample mean?"
Any thoughts on how I can compute this trust in a manner that is statistically sound?
Edit: changed 'median' to 'mean'.