Keeping in view of the objectives of averages, let us try to understand the requisites of an ideal average As suggested by the eminent statisticians Yule and Kendall, an ideal average should possess the following characteristics:
1) Easy to understand and simple to compute: It should be easy to make out an average and its computation should also be simple.
2) Rigidly defined: An average should be rigidly defined by a mathematical formula so that the same answer is derived by different persons who try to compute it. It should not depend on the personal prejudice or bias of a person computing it.
3) Based on all items in the data: For calculating an average, each and every item of the data set should be included. Not a single item should be dropped, otherwise the value of the average may change.
4) Not to be unduly affected by extreme items: A single extreme value i.e., a maximum value or a minimum value, can unduly affect the average. A too small item can reduce the value of an average, and a too big item can inflate its value to a large extent. If the average is changing with the inclusion or exclusion of an extreme item, then it is not a truly representative value of the data set.
5) Capable of further algebraic treatment: An average should be amenable to further algebraic treatment. That should add to its utility. For example, if we are given the averages of three data sets of similar type, it should be possible to obtain the combined average of all those three data sets.
6) Sampling stability: The average should have the same ‘sampling stability’. This means that if we take different samples from the aggregate, the average of any sample should approximately turn out to be the same as those of other samples.
