Price Index Number Calculation using the Method of Relatives

To calculate the price index number using the method of relatives, we need to follow the steps outlined below:

Step 1: Identify the Base Year
The first step is to identify the base year, which is the year against which all other years will be compared. In this case, the base year will be given in the table.

Step 2: Determine the Base Year Quantities and Prices
Next, we need to determine the quantities and prices of the items in the base year. These values will be used as the reference point for calculating the price index.

Step 3: Calculate the Relative Prices
In this step, we calculate the relative prices by dividing the prices of each item in a given year by the prices of the same items in the base year. This will give us the relative price ratio for each item.

Step 4: Calculate the Arithmetic Mean
After calculating the relative prices, we need to find the arithmetic mean of these values. The arithmetic mean is obtained by summing up all the relative prices and dividing the sum by the total number of items.

Step 5: Multiply by 100
Finally, we multiply the arithmetic mean by 100 to obtain the price index number. This number represents the percentage change in prices compared to the base year.

Now, let's apply these steps to the given table:

| Year | Item A | Item B | Item C |
|------|--------|--------|--------|
| 2018 | 10 | 15 | 20 |
| 2019 | 12 | 18 | 22 |
| 2020 | 15 | 20 | 25 |

Step 1: Identify the Base Year
In this case, the base year is 2018.

Step 2: Determine the Base Year Quantities and Prices
The quantities and prices for the base year are as follows:
- Item A: Quantity = 10, Price = 10
- Item B: Quantity = 15, Price = 15
- Item C: Quantity = 20, Price = 20

Step 3: Calculate the Relative Prices
To calculate the relative prices, we divide the prices of each item in a given year by the prices of the same items in the base year. The relative prices for each year are as follows:
- 2019 (Relative Prices): Item A = 12/10 = 1.2, Item B = 18/15 = 1.2, Item C = 22/20 = 1.1
- 2020 (Relative Prices): Item A = 15/10 = 1.5, Item B = 20/15 = 1.3, Item C = 25/20 = 1.25

Step 4: Calculate the Arithmetic Mean
To find the arithmetic mean, we sum up all the relative prices and divide by the total number of items. In this case, we have 3 items.
- Arithmetic Mean = (1.2 + 1.2 + 1.1 + 1.5 + 1.3 + 1.25) / 6 =