What Is a Capitalization-Weighted Index?
The weighted average index number is another form of calculating the total index. It is calculated by weighting the individual index with the total amount of a period as the weight. Its basic characteristic is: first calculate the individual index of each single item, and then weight the average of these individual indexes to obtain the total index. The purpose of weighting is to measure the different effects of changes in the price (or volume) of different commodities on the overall index.
Weighted average index
Right!
- The weighted average index number is another form of calculating the total index. It is calculated by weighting the individual index with the total amount of a period as the weight. Its basic characteristic is: first calculate the individual index of each single item, and then weight the average of these individual indexes to obtain the total index. The purpose of weighting is to measure the different effects of changes in the price (or volume) of different commodities on the overall index.
- Weighted average index is one of the methods to calculate the total index. It differs from the composite index in that: the starting point is different; the data requirements are different; the weights chosen can be different. The weighted arithmetic average method is commonly used to calculate the quantity index, and the weighted harmonic average method is used to calculate the quality index. In actual work, the average index has given new content, that is, the average index as a fixed weight, which is often used to calculate the retail price index of goods and the industrial production index.
- Specific form of weighted average index
- The weighted average index is divided into the base period total weighted index, the reporting period total weighted index, and the fixed weighted weighted index due to the different periods of the weights.
- Weighted arithmetic mean index
- The weighted arithmetic mean index can be divided into the arithmetic mean index of the base option number and the arithmetic mean index of the fixed weight according to the form of the weight.
- (1) The arithmetic mean index of the number of base options.
- It is an index that calculates the weighted average of the individual index by using the total value of the base period total index value as the weight. The formula is as follows:
- In the formula, p and q represent the price and sales volume of the product respectively; 0 and 1 represent the base period and the reporting period; I represents the total index.
- (2) The arithmetic mean index of a fixed weight.
- In the weighted arithmetic average index widely used at home and abroad, the weight used is not a value index (p0q0 or p1q1) of the base period or reporting period, but some fixed weight (W). Fixed weight refers to the weight of a certain fixed period, that is, it can be based on comprehensive survey data or various related sampling survey data. It can be fixed in the form of relative number (proportion), which has been used for a considerable period Convenience. For example, the industrial production index compiled by the capitalist countries mostly uses the data on the proportion of value added in the industrial sector as the weight. The formula of the weighted arithmetic mean index in the form of a fixed weight is:
- In the above formula, W represents the weight of a certain period.
- 2. Weighted Harmonic Mean Index
- The weighted harmonic average index can also be divided into two types according to the weight form: the harmonic average index of the number of reported options and the harmonic average index of the fixed weight.
- (1) Report the harmonic average index of the number of options. It is an index that calculates the weighted average of individual indices using the value of the reporting period as the weight. The formula is as follows: