Theoretical vs Practical Use of G.M. and A.M. in Index Numbers

Index numbers are widely used in economics and other fields to measure the changes in the value of goods, services, or other variables over time. The most commonly used types of averages in the construction of index numbers are the arithmetic mean (A.M.), geometric mean (G.M.), and harmonic mean. Among these, G.M. is theoretically considered as the best average for constructing index numbers. However, in practice, A.M. is mostly used. Here's why:

Theoretical Basis

The theoretical basis for using G.M. in the construction of index numbers is based on the assumption that the relative changes in the values of a variable are more important than absolute changes. That is, the percentage changes in the values of a variable over time are more significant than the actual values themselves. In this context, G.M. is considered to be the appropriate measure of central tendency because it is based on the product of the values and is not affected by extreme values.

Practical Considerations

While G.M. may be theoretically superior, A.M. is mostly used in the construction of index numbers due to practical considerations such as:

1. Ease of Calculation: A.M. is easier to calculate than G.M., especially when dealing with large datasets.

2. Familiarity: A.M. is a widely known and familiar concept, while G.M. is relatively less known and understood.

3. Sensitivity: A.M. is more sensitive to changes in extreme values than G.M. Therefore, it is better suited to capture the impact of such changes on average values.

4. Interpretation: A.M. is easier to interpret and explain to non-experts than G.M.

Conclusion

In conclusion, while G.M. may be theoretically superior to A.M. in the construction of index numbers, A.M. is mostly used in practice due to its ease of calculation, familiarity, sensitivity to extreme values, and ease of interpretation. However, the choice of the appropriate average ultimately depends on the nature of the data and the objectives of the analysis.