Arithmetic Mean

The most popular and widely used measures for representing the entire data by one value is what most laymen call an ‘average’ and what the statistician call the arithmetic mean. Its value is obtained by adding together all the items and by dividing this total by the number of items.
Arithmetic mean may either be
(i)    Simple arithmetic means, or
(ii)    Weighted arithmetic mean.

Merits and Limitations of Arithmetic means

Merits:

Arithmetic mean is most widely used in practice because of the following reasons:

1.    It is the simplest average to understand and casiest to compute. Neither the analyzing of data as required for calculating median nor grouping of data as required for calculating mode is need while calculating mean.

2.    It is affected by the value of every item in the series.

3.    It is defined by a rigid mathematical formula with the result that everyone who computes the average gets the same answer.

4.    Being determined by a rigid formula, it lends itself to subsequent algebraic treatment better than the median or mode.

5.    It is relatively reliable in the sense that it does not vary too much when repeated samples are taken from one and the same population, at least not as much as some other kind of statistical description.

6.    The mean is typical in the sense that it is the centre of gravity, balancing the value on either side of it.

7.    It is a calculated value, and not based on position in the series.

Limitations:

1.    Since the value of mean depends upon each and every item of the series, extreme items, i.e., very small and very large items, unduly affects the value of the average.

2.    In a distribution with open-end classes the value of mean cannot be computed without making assumptions regarding the size of the class interval of the open-end classes. If such classes contain a large proportion of the values, then mean may be subject to substantial error. However, the values of the median and mode can be computed where there are open-end classes without making any assumptions about size of class interval.

3.    The arithmetic mean is not always a good measure of central tendency. The mean provides a “characteristics” value, in the sense of indicating where most of the values lie, only when the distributions of variable is reasonably normal (bell shaped) in case of U-shaped distribution the mean is not likely to serve a useful purpose.

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