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The field of outlier detection and treatment is considerable, and a rigorous mathematical discussion is well beyond any treatment that is possible here. Moreover, the practice in the treatment of analytical results is usually simplified, since the number of observations is often not very large. The two most common methods used by analysts to detect outliers in measured data are versions of the Q-test and Chauvanets criterion, both of which assume that the data are sampled from a population that is normally distributed.
Citation
CRC Handbook of Chemistry and Physics - 93rd Edition