Assertion (A) on Geometric Mean for Index Numbers

The assertion states that the Geometric Mean (GM) is theoretically considered the best average for constructing index numbers. This is generally accepted because index numbers often involve averaging ratios, rates of change, or values that are multiplied together. GM is mathematically suited for such multiplicative relationships and appropriately handles the compounding effects inherent in index calculations.

Reason (R) on Geometric Mean Usage

The reason suggests that the Geometric Mean is used when the range of observations is extremely large. While GM is less affected by extreme values compared to the Arithmetic Mean (AM), making it a more stable choice in such cases, this is not the fundamental reason for its theoretical suitability for index numbers. The core reason lies in its ability to average rates of change and multiplicative factors.

Analysis of Assertion and Reason

• Assertion (A): True. Geometric Mean is preferred for index numbers due to its suitability for averaging ratios and handling multiplicative changes.
• Reason (R): True. GM is indeed less sensitive to extreme values than AM, making it a better choice when the data range is wide. However, this is a consequence of its properties rather than the primary theoretical reason for its use in index construction.
• Relationship: Reason (R) explains a scenario where GM might be practically useful due to its robustness, but it does not explain the core theoretical reason (multiplicative nature of data) why GM is considered the 'best' average for index numbers.

Conclusion

Both statements are true, but the reason provided does not correctly explain the assertion. The theoretical advantage of GM for index numbers stems from its handling of multiplicative relationships, not solely its ability to cope with large ranges.