Index Numbers using the Geometric Mean (GM) method

The GM method is one of the methods used for calculating index numbers. The formula for calculating index numbers using the GM method is as follows:

Index Number = (Current year value/Base year value)^(1/n) x 100

Where n is the number of commodities.

In this case, we have two commodities: A and B.

Using the data provided, we can calculate the index numbers as follows:

For commodity A:

Index Number = (55/25)^(1/2) x 100
Index Number = 2.213 x 100
Index Number = 221.3

For commodity B:

Index Number = (45/30)^(1/2) x 100
Index Number = 1.225 x 100
Index Number = 122.5

Therefore, the index numbers for commodities A and B using the GM method are:

- Commodity A: 221.3
- Commodity B: 122.5

Explanation of the GM method

The GM method is a method used to calculate index numbers. It involves finding the geometric mean of the ratio of current year values to base year values for each commodity. The geometric mean is a type of average that is calculated by taking the nth root of the product of n numbers.

In this case, we have two commodities, so we take the geometric mean of the ratio of current year values to base year values for each commodity. We then raise this to the power of 1/n, where n is the number of commodities. Finally, we multiply this by 100 to get the index number.

The GM method is useful because it takes into account the relative changes in the values of the commodities. It is also less affected by outliers than other methods, such as the arithmetic mean method.

Conclusion

The index numbers for commodities A and B using the GM method are 221.3 and 122.5, respectively. The GM method is a useful method for calculating index numbers because it takes into account the relative changes in the values of the commodities and is less affected by outliers than other methods.