The Weighted Average of Price Relative of Commodities

The weighted average of price relative of commodities is an important concept in economics and finance. It is used to calculate various index numbers, such as the consumer price index (CPI) and the wholesale price index (WPI), which are used to measure changes in the overall price level of goods and services in an economy.

Definition of Price Relative
A price relative is a ratio that compares the price of a commodity in a given year with its price in a base year. It is calculated by dividing the current year's price by the base year's price.

Definition of Weighted Average
A weighted average is an average in which each value is multiplied by a weight before being summed up. The weights are typically proportional to the importance or value of each value in the average.

The Formula
The formula for calculating the weighted average of price relative of commodities is as follows:

Weighted Average = [(Price Relative 1 * Value 1) + (Price Relative 2 * Value 2) + ... + (Price Relative n * Value n)] / (Value 1 + Value 2 + ... + Value n)

Explanation
- The weighted average of price relative of commodities is calculated by multiplying each price relative by its corresponding value and summing up the results.
- The weights used in the calculation are equal to the values of the commodities in the current year. This means that the importance or contribution of each commodity to the overall average is proportional to its value.
- The numerator of the formula represents the sum of the weighted price relatives, while the denominator represents the sum of the values.
- Dividing the sum of the weighted price relatives by the sum of the values gives us the weighted average of price relative of commodities.
- This weighted average can then be used to calculate various index numbers by multiplying it by a base value or dividing it by a base value and multiplying by 100 to express the result as a percentage.
- The resulting index numbers provide a measure of the average price level of the commodities included in the calculation, relative to a base year.

Conclusion
The weighted average of price relative of commodities, when the weights are equal to the value of commodities in the current year, yields index numbers that reflect changes in the overall price level of goods and services. It takes into account the importance or value of each commodity in the calculation, providing a more accurate measure of price changes.