There are two main objectives of the study of averages:

(i) To get single value that describes the characteristic of the entire group measures of central value, by condensing the mass of data in one single value, enable us to get a bird’s-eye view of the entire data. Thus one value can represent millions, billions and even millions of values. For example, it is impossible to remember the individual incomes of mullions of earning people of Indian and even if one could do it there is hardly any use. But if the average income is obtained by dividing the total national income by total population we get one single value that represents the entire population. Such a figure would throw light on the standard of living of an average Indian.

(ii) To facilitate comparison measures of central value, by reducing the mass of data to one single figure, enable comparison to be made. Comparison can be made either at a point of time or over a period of time. For example, we can compare the percentage results of the students of different colleges which college is the best or we can compare the pass percentage of the same college for different time periods and thereby conclude as to whether the results are improving or deteriorating, such comparison are of immense help in framing suitable in timely policies. For example. If the pass percentage of students in college a in b. com. Was 80 in 2008 and 75 in 2009, the authorities have sufficient reason for investigating the possible cause of the deterioration in results.

However, while making comparisons one should also take into consideration the multiplicity of forces that might be affecting the data for example, if per capita income is rising in absolute terms from one period to another, it should not lead one to think that the standard of living is necessarily improving because the prices might be rising faster than the rise in per capita income and so in real terms people might be worse off. Moreover’ the same measure should be used for making comparison between two or more groups. For example, we should not compare the mean wage of one factory with the median wage of another factory for drawing any inference about wage levels.

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) Easy to understand: since statistical methods are designed to simplify complexity, it is desirable that an average be such that can be readily understood; otherwise its use is bound to be very limited.

(ii) Simple to compute: an average should not only be easy to understand but also simple to compute so that it can be used widely. However, though ease of computation is desirable, it should not be sought at the expense of other advantages, i.e. if in the interest of greater accuracy, use of a more difficult average is desirable, and one should prefer that.

(iii) Based on all the items: the average should depend upon each and every item of the series so that if any items is dropped the average itself is altered. For example, the arithmetic mean of 10, 20, 30, 40, and 50 is. 10 + 20 + 30 +40 + 50/5 = 150/5 = 30. If we drop one item, say, 50, the arithmetic mean would be = 25.

(iv) 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 disort the average and reduce its usefulness.

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