The choice of an average is an important problem which a statistician has to face. This necessitates a relative evaluation of these three measures of central tendency.
We have discussed earlier the characteristics of a good average. All the characteristics of a good average are satisfied by Arithmetic mean. Hence it is widely used as the average. But it has got its demerits. Likewise, median and mode have got their relative merits and demerits. Choice of the average depends upon the following considerations.
(a) The object or purpose of enquiry:
If all values in a series are to be treated as equally important, the arithmetic mean will be the most suitable average, while median and mode will be highly unsuitable. If the purposes is to locate the most common item of a series, mode should be used. If the purpose is to study the average of qualitative phenomena, median should be chosen. Graphic presentation of data is more appealing. Hence if graphic presentation is desired, then median or mode should be selected.
(b) Whether the average is used for further algebraic treatment:
If it is to be used for further statistical analysis, arithmetic mean should be chosen as average. Arithmetic mean is capable of further algebraic treatment.
(c) The nature of the data:
Arithmetic mean is not an ideal average for distributions with extreme items or open-end classes. In such cases, median and mode are better averages. When a series is constituted with unequal class-intervals there will be no problem for computation of arithmetic mean and median. They can be computed straightaway. But mode cannot be determined from such a series without equalizing the class intervals. If there is great variability amongst the items, median will not be representative. Arithmetic mean will be more suitable. In conclusion, it can be said that proper and judicious choice of average for a particular problem is very important.