Measures of Central Tendency or Averages have been defined differently by different statisticians.
“A measure of Central tendency is a typical value around which other figures congregate.” —Simpson and Kafka
“An average stands for the whole group of which it forms a part, yet represents the whole”. —A.E. Waugh
“An average is a figure that represents the whole group.” —Clark
Thus the basic purpose of the statistical analysis is to determine the value which represents the whole series. This value is termed as central value or an average. In other words, average is a statistical measure representing a group of individual values in simple and comprehensive manner.
Objectives and Functions of Averages:
(i) Representative of the group:
An average represents all the features of a group; hence the results about the whole group can be deduced from it.
(ii) Brief Description:
An average gives us simple and brief description of the main features of the whole data.
(iii) Helpful in comparison:
The measures of central tendency or averages reduce the data to a single value which is highly useful for making comparative studies. For example, comparing the per capita income of two countries, we can conclude that which country is richer.
(iv) Helpful in formulation of policies:
Averages help to develop a business in case of a firm or help the economy of a country to develop.
(v) Base of other statistical Analysis:
Other statistical devices such as mean deviation, co-efficient of variation, co-relation, analysis of time series and index numbers are also based on the averages.