Characteristics of a Good Average
(i) It should be rigidly defined. If an average is left to the estimation of an observer and if it is not a definite and fixed value it cannot be representative of a series. The bias of the investigator in such cases would considerably affect the value of the average. If the average is rigidly defined; this instability in its value would be no more, and it would always be a definite figure,
(ii) It should be based on all the observations of the series. If some of the items of the series are not taken into account in its Calculation the average cannot be said to be a representative one. As we shall see later on there are some averages which do not take into account all the values of a group and to this extent they are not satisfactory averages.
(iii) It should be capable of further algebraic treatment. If an average dose not possess this quality, its use is bound to be very limited. It will not be possible to calculate, say, the combined average of two or more series from their individual averages; further it will not be possible to study the average relationship of various parts of a variable if it is expressed as the sum of two or more variables. Many other similar studies would not be possible if the average is not capable of further algebraic treatment.
(iv) It should be easy to calculate and simple to follow. If the calculation of the average involves tedious mathematical processes it will not be readily understood and its use will be confined only to a limited number of persons. It can never be a popular average. As such, one of the qualities of a good average is that it should not be too abstract or mathematical and there should be no difficulty in its calculation. Further, the properties of the average should be such that they can be easily understood by persons of ordinary intelligence.
(v) It should not be affected by fluctuations of sampling. If two independent sample studies are made in any particular field, the averages thus obtained, should not materially differ from each other. No doubt, when two separate enquires are made, there is bound to be a difference, in the average values calculated but in some cases this difference would be great while in others comparatively less. These averages in which this difference, which is technically called "fluctuation of sampling" is less, are considered better than those in which its difference is more.
One more thing to be remembered about averages is that the items whose average is being calculated should form a homogenous group. It is absurd to talk about the average of a man's height and his weight. If the data from which an average is being calculated are not homogeneous, misleading conclusions are likely to be drawn. To find out the average production of cotton cloth per mill, if big and small mills are not separated the average would be unrepresentative. Similarly, to study wage level in cotton mill industry of India, separate averages should be calculated for the male and female workers. Again, adult workers should be separately studied from the juvenile group. Thus we see that as far as possible, the data from which an average is calculated should be a homogeneous lot. Homogeneity can be achieved either by selecting only like items or by dividing the heterogeneous data into a number of homogeneous groups.
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