Averaging Objectives

There are two important objectives of the study of averages:

(i) To get a single value that describes the characteristic of the whole group measures of the central value, by condensing the mass of data into one single value, enable us to get a bird's-eye view of the whole  data. Thus one value can shows  millions, billions and even millions of values. For e.g. , it is impossible to remember the individual incomes of millions 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 the total population we get one single value that shows  the entire population. Such a figure would throw a light on the standard of living of an average Indian.

(ii) To facilitate the comparison measures of central value, by reducing the mass of data to one single figure, enable comparison to be made. The Comparison can be made either at a point of time or over a period of time. For e.g. , we can compare the percentage results of the students of various colleges which college is the best or we can compare the pass percentage of the similar college for different time periods and thereby conclude as to whether the results are improving or not, such comparison are of immense help in framing suitable in timely policies. For e.g. If the pass percentage of students in 'a' college  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 taking the  comparisons one should also take into consideration the multiplicity of forces that might be affecting the data for e.g. , if per capital  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 as  the prices might be rising faster than the rise in per capital  income and so in real terms people might be worse off. Moreover' the same measure must be used for making comparison between two or more groups. For e.g. , we must  not compare the mean wage of one factory with the median wage of another factory for drawing any inference about wage levels.

The Requisites of a good average

Since an average is a single value representing a group of values, it is desired that such a value fulfill  the following properties:

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

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

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

(D) Not be unduly affected by extreme observations: Although each and every item must influence the value of the average, none of the items should influence it unduly. If one or two very small items  or very large items unduly affect the average, i.e. either increase its value or decrease its value, the average cannot be really typical of the whole  series. In another words, extremes may distort the average and reduce its usefulness.