Calculation of Index Numbers using the Geometric Mean Method

To calculate the index numbers using the Geometric Mean (GM) method, the following steps need to be followed:

Step 1: Identify the base year and the current year
In this case, the base year is the year for which the index is calculated, and the current year is the year for which the comparison is made. Let's assume the base year is the "base year" and the current year is the "current year".

Step 2: Calculate the price relatives
Price relatives are calculated by dividing the current year price by the base year price for each commodity. The formula to calculate the price relative is:

Price Relative = (Current Year Price / Base Year Price) x 100

For commodity A, the price relative is calculated as:
Price Relative for A = (55 / 25) x 100 = 220

For commodity B, the price relative is calculated as:
Price Relative for B = (45 / 30) x 100 = 150

Step 3: Calculate the geometric mean
The geometric mean is calculated by taking the nth root of the product of price relatives, where n is the number of commodities. The formula to calculate the geometric mean is:

Geometric Mean = (Price Relative for A x Price Relative for B)^(1/n)

In this case, n = 2 (as there are two commodities).

Geometric Mean = (220 x 150)^(1/2) = 181.765

Step 4: Calculate the index number
The index number is calculated by multiplying the geometric mean by 100. The formula to calculate the index number is:

Index Number = Geometric Mean x 100

Index Number = 181.765 x 100 = 18176.5

Step 5: Round off the index number
The index number should be rounded off to the nearest two decimal places. In this case, the index number rounded off to two decimal places is:

Index Number = 181.77

Answer:
From the given data, the index number using the Geometric Mean method is 181.77.

Explanation:
The Geometric Mean method is used to calculate the index numbers by taking the geometric mean of the price relatives. The price relatives are calculated by dividing the current year price by the base year price for each commodity. The geometric mean is then calculated by taking the nth root of the product of price relatives. Finally, the index number is calculated by multiplying the geometric mean by 100 and rounding off to the nearest two decimal places. In this case, the index number is 181.77.