Outlier tests must be carried out before each calculation of statistical quantities in order to check the quality of the measurements. A data point that qualifies as an outlier must not be taken into account in further calculations under any circumstances, as otherwise you will get incorrect results. Such tests may only be performed once in a data set—this is partly because outliers are indeed rare events and partly because taking out values would then change the distribution a lot. Imagine that you spot two suspicious measurement points A and B. If you actually eliminate A in a first step, then the characteristic values (mean and standard deviation) of the distribution change in such a way that candidate B fits all at once. If, on the other hand, you start with candidate B, then it is possible that this point is an outlier on the basis of the distribution, and accordingly the point is excluded from further considerations. But what happens with point A, possibly this point now fits the remaining distribution. You can see the dilemma here when you examine suspicious measurement points one after the other for their outlier properties.