Requisites of a Good Average
Since an average is a single value representing a group of values, it is desired that such a value satisfies the following properties:
(i) It should be easy to understand.
Since statistical methods are designed to simplify complexity. It is desirable that an average is such that can be readily understood; otherwise, its use is bound to be very limited.
(ii) It should be simple to compute.
Not only an average should be easy to understand but also it should be simple to compute so that it can be used widely. However, though ease of computation is desirable is should not be sought at the expense of the other advantages, i.e., if in the interest of greater accuracy, use of a more difficult average is desirable, one should prefer that.
(iii) It should be based on all the items.
The average should depend upon each and every item of the series so that if any of the items is dropped the average itself is altered.
(iv) It should not be unduly affected by extreme observations.
Although each and every item should influence the value of the average, none of the items should influence it unduly. If one or two very small or very large items unduly affect the average, i.e., either increase its value or reduce its value, the average cannot be really typical of the entire series. In other words. Extremes may distort the average and reduce its usefulness.
(v) It should be rigidly defined.
An average should be properly defined so that it has one and only one interpretations. It should preferably be defined by an algebraic formula so that if different people compute that average from the same figures they all get the same answer (barring arithmetical mistakes). The average should not depend upon the personal prejudice and bias of the investigator; otherwise the results can be manipulated.
(vi) It should be capable of further algebraic treatment.
We should prefer to have an average that could be used for further statistical computations so that its utility is enhanced.
(vii) It should have sampling stability.
Last, but not the least, we should prefer to get a value which has what the statisticians call ‘sampling stability’ This means that if we pick 10 different groups of college students, and compute the average of each group, we should expect to get approximately the same value. It does not mean, however, that there can be no difference in the values of different samples. There may be some difference but those samples in which this difference (technically called sampling fluctuation) is less are considered better than those in which this difference is more.
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