Both the mean and the median satisfy the conditions of rigid definition and stability but so far as ease in calculation is concerned median has a distinct advantage over mean. On the other hand, the general fluctuations of sampling affect the median to a greater extent than the mean, though there might be cases where mean is affected to a greater extent by such fluctuations than the median.

 So far as the case of algebraic treatment of these two averages is concerned, mean is definitely superior to median. In case of mean when several series relating to one phenomenon are combined into one, it is possible to find out the combined averages from the averages of various series and their number of observations. It is not possible in case of median. However, if the component series are symmetrical their means and medians would also be the same. But in case of asymmetrical distribution the combined median would not coincide with the mean or with any other assignable value. The sum or difference of the corresponding values of the items of two series is not equal to the sum or difference of their medians as is the case with arithmetic average. The calculated value of the median subject to error is not necessarily the same as the true value of the median, even if the error is zero, that is, if positive or negative errors cancel each other.

On the other hand, median has certain advantages over the mean. It is easily calculated and is readily obtained without even knowing the value of all the items, provided they can be arrayed. Further in some cases mean cannot be calculated due to the extreme class intervals being infinite, like "less than 100" or "more than 10,000", etc., but median can be easily obtained in such distributions. Sometimes median may be more representative than the arithmetic average due to the fact that it is not affected by the values of extreme items. If for example, the values of most of the items of a sample cluster round 200, median would not be affected, if suddenly one item, whose value is 3000, is included in the sample. Mean in such cases is more affected by fluctuations of sampling than the median. Further, median is generally the value of a particular item of the series, whereas mean may not be the value of any item of the series. In this sense median is a more natural average than the mean.