We are doing a lab test where one of the criteria for the material being tested to "pass" is:
no individual specimen shall deviate more than 3 standard deviations from the mean for the 10 specimens
I can’t for the life of me create a set of data where 1 specimen is outside of 3 standard deviations. The data points we are dealing with is “percent mass loss” so by definition it is constrained to zero to one.
I am beginning to think it might not be possible to have a set of data that fails the test for this criteria.
Am I correct in saying:
An outlier has such a strong influence on the standard deviation that the "mean+3*stdev maximum" always is greater than the outlier itself when the size of the dataset is 10.