# Getting a single-value estimation of trust in a computed mean

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'.

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the median and stddev will be different Are you actually thinking of the median or the mean (expected value)? – leonbloy Jul 8 '11 at 13:59
Yes, I meant the "mean". Sorry, English is not my first language. – Jon Smark Jul 8 '11 at 15:07
Normality assumption is unreasonable. Do not understand meaning of $\mu$ and $\sigma$ being different "for each one." But put as a confidence interval problem, sample mean should, except for very small samples, have a normal enough distribution, and usual techniques will work well enough. – André Nicolas Jul 8 '11 at 18:40