> This may seem like a trivial question, but if the dataset contains all > whole numbers -- 2,3,5,7,21,23,34,35,etc, etc, > then is there anything at all that can be said about the number of > significant digits for the corresponding mean of the sample? > > My reading is that the mean is unconstrained regarding the significant > digits that it can have; however, a collegue suggested that the mean can > only be as significant as the data contained in the sample set.
Whoops - the thread is already considerably long, so all I might add is: have you considered using the median instead of the mean ? If the data are integers not only because of measurement inaccuracy but because the random process does produce integers only, you have an alternative measure of location in the median which does have some appeal of its own (robustness to outliers, e.g.). I do recall that my maths teacher at school strongly refused to provide the mean of all grades when he returned our exams, but insisted on giving the median instead. He had his reasons.