Arithmetic mean is the number which is obtained by adding the value of all items of a series and dividing the total by the number of items.
1. Simple arithmetic mean
2. Weighted arithmetic mean
Simple arithmetic mean
(1) Direct method
It involves the following steps:-
(a) Value of the various items in the series are indicated by x, and their frequencies by ‘f’
(b) Each item is multiplied by its frequency to get ‘f’ and ‘x’ these multiple are added to get FX.
Short cut method:
Before calculating the actual average of the series, some value which lies in the middle of the series is taken as assumed average.
Step deviation method:
This method is variant of the short cut method. It is adopted when deviation from the assumed mean have some common factor. A notable property of arithmetic mean is that the sum of deviations of different items of a series, when deviations are taken from arithmetic mean, is always zero.
Merits of arithmetic mean
- From the view point of calculation and usage, arithmetic mean is the simplest of all the measurers of central tendency.
Arithmetic mean is a certain value; it has no scope for estimated values.
Based on all items:
- It is based on all items in a series. It is, therefore, a representative value of the different items.
- It is capable of further algebraic treatment. It is, therefore, extensively used in statistical analysis.
- It is a stable measure of central tendency. This is because changes in the simple of a series have minimum effect on the arithmetic average.
Basis of comparison:
- Being stable and certain, arithmetic mean can be easily used for comparison.
- It can be tested for its accuracy as a representative value of the series.
Demerits of arithmetic mean
Following are the various demerits of arithmetic mean:
Effect of extreme value:
- The main defect of arithmetic mean is that it gets destroyed by extreme value of the series. Therefore, it is not always an accurate measure.
Mean value nay not figure in the series at all :
- The mean value may sometimes be that value which does not figure in the series at all.
- It is sometimes offer laughable conclusion.
- It is not a suitable measure in case of percentage or proportionate values.
- Arithmetic mean sometimes offers misleading conclusion.
However, despite certain demerits of arithmetic mean as noted above, this is an ideal measure of the central tendency. This is most widely used measure in practical life. Arithmetic mean is particularly significant in such series of which different items are equally important and, therefore, equally weighted. Average output, average cost, average revenue, are some of the well known concepts in economics based on arithmetic mean.
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