# Arithmetic Mean

The word average, we use every frequently in day-to-day expressions.  Such as average price, average income, average weight etc.  In these expressions the word average is nothing but arithmetic mean.  Generally a layman call an average but a statistician call the arithmetic mean. The arithmetic mean is commonly known as mean. It is a measure of central tendency because other figures of the data congregate around it. Arithmetic mean is obtained by dividing the sum of the values of all observations in the given data set by the number of observations in that set. It is the most commonly used statistical average in the disciplines such as commerce, management, economics, finance, production, etc. The arithmetic mean is also called as simple Arithmetic Mean.

Merits and Limitations of Arithmetic Mean

The arithmetic mean has the following merits and limitations:

Merits:

1) It is easy to understand and simple to compute.  It is the widely used summary measure.

2) It is rigidly defined.

3) It acts as a single representative figure of the whole data set.

4) It is based on all items of the data.  It does not depend on its position in the series.

5) It leads itself to further mathematical treatment.

6) It is useful in further statistical analysis.  It is used in computation of other statistical measures like standard deviation, coefficient of variation, co-efficient of skewness, etc.

7) It is characterised as a centre of gravity – a point of balance.

8) For various sampling methods, the simple mean is an unbiased estimate of the population mean.

Limitations:

1) It is unduly affected by extreme values.  Very small and very big values in the data unduly affect the value of mean. Therefore, for the distribution where concentration is on small or big values, the mean will not be a proper average to yield a representative figure.

2) For the open-ended distributions, mean cannot be computed with accuracy.  For example, in an income distribution starting with the class ‘below 500’ and ending with the class ‘above 5,000’ mean cannot be computed without making assumptions regarding the values of two extremes.  As a result, error may creep in.

3) Mean is not useful for studying the qualitative phenomena e.g., beauty, honesty, intelligence, etc.

4) For the reasonably norms (bell shaped) distribution, mean can act as a good measure of central tendency.   But for a U-shaped distribution (which has high frequency in the beginning, low in the middle and again high towards the end) it hardly succeeds to be a point of location around which other individual values congregate.

5) Mean does not lead a life of its own.  For example, the statement that the average number of children in Indian family is 4.8 does not imply that there is even a single family having 4.8 children.  Nor was a duck ever killed by the average of two shots – one a yard in front of it and one a yard behind it.

6) For non-homogeneous data, average may give misleading conclusion. For example, sales (in lakh rupees) of two business units A and B during the last five years are as follows:

A:  30 25 20 15 10

B:  10 15 20 25 30

Here it is clear that the average sales of both the units are exactly the same and yet unit B is thriving whereas unit A is flickering.