Merits and Demerits of Geometric Mean

The merits and demerits of the G.M. can be outlined in the light of the characteristics of an ideal average as follows:

Merits

1. It is rigidly defined.
2. It is based on all the observations of the series.
3. It is suitable for measuring the relative changes.
4. It gives more weights to the small values and less weights to the large values.
5. It is used in averaging the ratios, percentages and in determining the rate gradual increase and decrease.
6. It is capable of further algebraic treatment. As such, if the G.M. and the number of items of two or more series are given, we can readily find out the combined G.M. of all the series by the following formula:G1.2 = AL { N1 log G1 + N2 log G2/ N1+ N2 }For example, see the illustration 54.

Demerits

1. It is not easy to understand by a man of ordinary prudence as it involves logarithmic operations. As such it is not popular like that of arithmetic average.
2. It is difficult to calculate as it involves finding out of the root of the products of certain values either directly, or through logarithmic operations.
3. It cannot be calculated, if the number of negative values is odd.
4. It cannot be calculated, if any value of a series is zero.
5. At times it gives a value which may not be found in the series, and may even be assured or impracticable.