  Introduction

An average or central value is a single value that represents all the items in a series or a set of data. It is also called measure of central tendency. The main objectives or purposes of averages are: it represents the whole data; it describes the basic features of the group of data, etc. The characteristics of a representative average are: it is rigidly defined, based on all the observations and it is simple to calculate, etc. The averages are broadly classified as: mathematical averages and positional averages. The mathematical average is further divided into arithmetic mean, geometric mean and harmonic mean. The positional average is divided into median, quartile and mode.

The most commonly used measure of central tendency is mean. It is the sum of all the numbers in the series divided by the number of items in a series. Different methods (direct method, assumed mean method and step deviation method) are being used for calculation of mean under different types of data (grouped and ungrouped-Discrete series and continuous series).

Apart from these there are some special cases of arithmetic mean like cumulative frequency distribution, open ended, correcting incorrect value, missing value and missing item or frequency. Weighted arithmetic mean refers to the average when different items of a series are given different weights according to their relative importance. Properties of arithmetic mean are: algebraic sum of deviations of items in a series from their arithmetic mean is zero, product of arithmetic mean and the number of observations on which the mean is based is equal to the sum of all the given values and we can compute the combined average or mean of two groups, given the arithmetic mean and the number of items of two or more than two related groups. The various merits of arithmetic mean are: the value of arithmetic mean is always definite and certain, it is based on all the observations, it is capable of further algebraic treatment, etc.

Arithmetic mean cannot be calculated unless all the items of a series are known, and this is the biggest demerit of arithmetic mean. 