within 2-sigma

here is a primer

http://www.ece.rochester.edu/courses/ECE111/error_uncertainty.pdf

there are a lot of books that go into more detail

Or you can use the outlier labeling rule by Tukey: upper limit = Q3+(Q3-Q1)*g and lower limit = Q1-(Q3-Q1)*g. Q stands for quartile. For more information please review the following YouTube page:

https://www.youtube.com/watch?v=WSflSmcNRFI

I think the question is with reference to standard error acceptability and not about the statistics (usually mean) about which the standard error is estimated. It is simply thinking of measuring the quality of student by evaluating the teacher (rather than evaluating the student).

Standard error is used to evaluate how best a sample statistics, say sample mean, represents the underlying population – population mean in case the statistics to evaluate is the sample mean. Building confidence interval around the sample mean, using 2 times standard error is the common practice to evaluate the sample mean.

Now, how to evaluate the standard error. No way. However, you can work on squared SEs. How? Do simulations. By drawing independent samples from the same population say, 100,000/- times you will be able to go to all these sample indecently and get all the 100,000/- samples’ distribution of squared SEs. From which you can set critical value for squared standard error based on say 95 confidence level. In my opinion it will be a sort of chi-square distribution and test should be one sided. Simply because: Distribution of variance is usually chi square. And, to see for best sample results you would like to minimize the squared variance and not the other way round.

The standard error of a sample mean (taken as the measured value) is a measure of the quality of the measurement. It is known as the Type A standard uncertainty according to the GUM. You may also use the relative standard error to assess your measurement quality, if the quantity to be measured cannot be negative. Whether a standard error (or the measured value) is acceptable depends on your application, or uncertainty-based measurement quality control criterion. In our field of river discharge measurements, the acceptance criterion is about 2% in terms of relative standard error.