Page 125 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 6.6.6 Properties of Geometric Mean

1. As in case of arithmetic mean, the sum of deviations of logarithms of values from the log
GM is equal to zero.
This property implies that the product of the ratios of GM to each observation, that is less
than it, is equal to the product the ratios of each observation to GM that is greater than it.
For example, if the observations are 5, 25, 125 and 625, their GM = 55.9. The above property
implies that

55.9 55.9 125 625
5 25 55.9 55.9
2. Similar to the arithmetic mean, where the sum of observations remains unaltered if each
observation is replaced by their AM, the product of observations remains unaltered if
each observation is replaced by their GM.

6.6.7 Merits, Demerits and Uses of Geometric Mean

Merits

1. It is a rigidly defined average.
2. It is based on all the observations.
3. It is capable of mathematical treatment. If any two out of the three values, i.e., (i) product
of observations, (ii) GM of observations and (iii) number of observations, are known, the
third can be calculated.
4. In contrast to AM, it is less affected by extreme observations.
5. It gives more weights to smaller observations and vice-versa.

Demerits

1. It is not very easy to calculate and hence not very popular.
2. Like AM, it may be a value which does not exist in the set of given observations.

Uses

1. It is most suitable for averaging ratios and exponential rates of changes.
2. It is used in the construction of index numbers.

3. It is often used to study certain social or economic phenomena.

Task Calculate AM, GM and HM of first five multiples of 3.Which is greatest? Which is
smallest?

! Geometric mean cannot be calculated if any observation is zero or negative.
Caution

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