There are certain variables that we cannot count or quantify in absolute terms. To measure such variables we use specialized averages known as index numbers. There are three main types of index numbers – price, quantity, and value index number. Let us learn more.

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## What are Index Numbers?

As per the famous economist Bowley, Index numbers are “numbers used to measure the changes in some quantity which we cannot observe directly”. It is a statistical tool to measure changes and variations in a variable (or even a group of variables) with respect to time or any such other aspect (geography, location, etc).

#### Some important characteristics of index numbers are as follows,

- These are special averages. Other statistical averages like mean, median and mode measure the absolute changes of a given series of data. However, when such a measure of absolute variation is not possible we use index numbers. They measure the relative changes/variation in the level of a phenomenon.
- Index numbers help us study the factors which cannot be measured directly. For example, there is no measure to measure the general price level in the market. But index numbers can help us measure the relative change or variation in the price levels.
- It also allows measuring the relative changes in a group of closely related variables.

#### There are essentially three broad classifications of index numbers as shown below,

- Price Index Number: Price index number is a scale used to measure changes in the level of prices in the economy. It compares the price of the current year, with that of the base year to give us an idea of the relative variation. It is a very good measure of inflation in the economy.
- Quantity Index Number: As the name suggests, this measures the changes in the quantities of goods between any two given years. This can be the number of goods produced, sold, consumed, etc. It is a good indication of the output of an economy.
- Value Index Number: This is an index number is the ratio of the aggregate value of a given commodity in the current year and its value in the chosen base year. We will learn more about this here.

## Value Index Number

The value index number compares the value of a commodity in the current year, with its value in the base year. What is the value of a commodity? It is nothing but the product of the price of the commodity and the quantity. So the value index number is the sum of the value of the commodity of the current year divided by the sum of its value in the chosen base year. The formula is as follows,

$$ v_{01}Â = \frac{\Sigma{p_1 q_1}}{\Sigma{p_0 q_0}} \times 100 $$

or alternatively,

$$ v_{01}Â = \frac{\Sigma{v_1}}{\Sigma{v_0}} \times 100 $$

In this case of a value index number, we do not apply any weights. Since these are considered to be inherent in the value of a commodity. Thus we can say that a value index number is an aggregate of values.

The value index number is not a very popular statistical tool. Price and quantity index numbers give a clearer picture of the economy for study and analysis. They even help in the formulation and implementation of economic policies.

## Question on Value Index Number

Q: In a value index number, what is the test of consistency?

Ans: As per the test of consistency, the product of the price and quantity index number must give us the value index number, as price into quantity produces the value.

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