Upper bound for the error on the mean for small samples.

[Wintersun]

I have a sample of an unknown distribution for which I would like an estimate of the mean and the error on that mean. For small samples the typical way of doing this breaks down. What is a reasonable way to estimate the mean and an upper bound of the error on the mean? The error on the mean will go into a fitting method so it is much more important to have an upper bound than an unbiased estimator.

Please include the range this should be applied over.

 

[EdGr]

Not sure what would work best for you. A bootstrap (Monte-carlo) method might be the best way to get bounds if the data are of some odd distribution. Many packages will do that for you. // If you have one or two outliers, you might want to try a trimmed mean (http://en.wikipedia.org/wiki/Truncated_mean). Note that this is not necessarily a good estimate for the actual mean, but may be more reliable than it.

 

[hlsmith]

I agree with EdGr's suggestions. Also, it may be informative if you describe what the distribution looks like and the actual small sample size.