Having thus, analysed the process of computation, the relative merits, and demerits of arithmetic average can be outlined in the light of the characteristics of an ideal average as under :
- It is rigidly defined and thus, there is no scope for ambiguity, or misunderstanding about its meaning and nature.
- It is easy to understand, and thus it is a popular or common men’s average.
- It is simple to calculate under any given order of the data, and thus it does not require the rearrangement of the series either in ascending, or in descending, or in grouping order as it is required in case of Median, Mode, Quartiles etc.
However, under the shortest method, the data need to be arranged in the ascending order, if give otherwise and in case of a cumulative series, it needs the rearrangement of the series in order of the class intervals, and their corresponding specific frequencies.
- It is based on all the items of a series as in its computation no item is ignored.
- It is not very much affected by fluctuations in sampling and thus, its result is relatively dependable.
- It is capable of further algebraic treatment, and thus in almost all the advanced studies of statistics like measures of dispersion, skewness, correlation, sampling etc. it is taken as a formidable factor.
- It has maximum mathematical properties, and thus the various factors involved in its formula can be computed easily under various methods viz. direct, short-cut, step deviation and shortest methods.
- It is calculated through and algebraic formula without reference to any position in the series.
- It is characterized as the point of balance, or the center of gravity from which the deviations of the items on both the sides are equal.
- It is greatly affected by the values of extreme items of a series, and thus it fails to give a representative value of the series. Thus, in an office, if there are 4 clerks, and 1 officer with monthly salaries of $300, 350, 400, 450 and $2000 respectively, their average salary will come to $700, i.e. .300+350+400+450+2000/5
Here, the average value has been inflated to $700, while 4 persons out of 5 are getting much less than $700.
This is because the average value has been affected much, here, by a single value of $2000, the salary of one officer only.
- At times, it gives a value which is not present in the series. Thus, the average of 3, 5 and 10 is 6 which is never in the series.
- At times it gives absurd and impracticable values. Thus, the average number of children of 3 families having 2, 4 and 5 children respectively would be 11/3 or 3.67 approx. which is never possible.
- It cannot be calculated in a distribution with open end classes without making assumptions on the size of the class intervals of the open end classes. This difficulty is not faced in case of other averages viz, Median, Quartiles, Mode etc.
- It fails to provide a characteristic value, or a representative item where the distribution of the series is not normal and gives a U shaped curve rather than a bell shaped one.