An index number in statistics is a tool that we generally use to measure the difference in relative changes from time to time. The difference can also be from place to place. It can be thought of as the arithmetic mean that we use to find or represent some values of a particular data set.

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**Index Number in Statistics**

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An index number is basically a ratio which has the involvement of more than two periods. For every index number, the base year remains the same. Some of the examples are CPI, WPI, BSE, etc.

An index number is generally of two types: simple and composite. When there is an involvement of a single variable, we call it a simple index. Similarly, when there is an involvement of two or more variables, it is composite.

**Browse more Topics under Index Numbers**

## Issues in Index Number

Some of the common problems that we come acrossÂ for constructing index numbers are as follows.

**Data SelectionÂ –Â**The purpose of an index is very important. Also, it is important to know the reasons why we are using it. Index numbers are generally the results of the sample. So, it is necessary that these index numbers are representative. Likewise, comparability is also important in this case.**Weight Selection –Â**It is important for the variables in the composite index to have their own influence particularly in the index. Hence, the importance should reach out to those variables that have a significance in the purpose of an index.

## Uses of Index Number in statistics

Well, now that we know the different types of index numbers, it is important to know their limitations as well. Here they are:

- The indices come out as a result of samples. These samples are mostly deliberate. As a result, there are valid chances for errors to swipe directly. Avoiding or preventing these errors can turn out to be a difficult job
- Index numbers are always based on items. Most of the times, these selected items show off the trend. Thus, hiding off the real story and the picture
- There are numerous methods that we use for the proper construction of index numbers. As a result of this, the outcomes brings different values which are likely to create a lot of confusion

As long as these limitations are taken care of there are several areas that bring out the uses of an index number in statistics. They are:

- Index numbers have a great use inÂ
*deflating.Â*Index numbers have the capacity to adjust the primary data at different costs. Therefore, it becomes easy to transform a nominal wage to real wage - Index numbers come up with several trends and tendencies that help with making important conclusions; conclusions in cyclical forces and irregular forces
- We also use index numbers in areas like economics. Index numbers help with framing the simple and suitable policies by providing guidelines. These guidelines also help to make decisions relating to research, quotients, and so on
- The use of index number helps in tackling the future enhancement of the economic activities. Most people use it in time series analysis to know more about the cycle developments, trends, and variations etc.
- Index numbers measure the changes happening in the standards of living over a given period of time

## Construction ofÂ an Index Number (Series)

**Notations:Â **Let P* _{n}*(

^{1}),Â P

*(*

_{n}^{2}),Â P

*(*

_{n}^{3}) etc are the general prices during a period of time for a different commodity. Here the period is 1st, 2nd, and 3rd. The base period price for the same isÂ –Â P

*(*

_{o}^{1}),Â P

*(*

_{o}^{2}),Â P

*(*

_{o}^{3}), etc. So, for the notations, the price of any commodity, say ‘j’ during a given time period ‘n’ isÂ P

*(*

_{n}^{j}). Here is the notation.

**âˆ‘ _{j=1}^{kÂ }P_{n}(^{j}) orÂ âˆ‘Â P_{n}(^{j})**

Removing the summations, we can writeÂ **âˆ‘P_{n}**

### Relatives

Price relative is one of the most simple examples of an index number. Price relative is the ratio of the amount of a specific commodity in a given time period to its other price in some other time period. This is the base period or reference period. The illustration of the same is as follows.

**Price Relative =Â P_{n}/P_{o}**

Furthermore, to convert it into a percentage value, we multiply it by 100.

**Price Relative =Â P_{n}/P_{o} * 100**

Quantities, consumption volume, exports, etc can be some of the other relatives. In such cases, the formula to calculate relative is:

**Quality Relative =Â Q_{n}/Q_{o}**

Similarly, there can be formulas for value relative:

**Value Relative =Â V_{n}/V_{oÂ }=Â P_{n}Q_{n}/P_{o}Q_{o}**

** Link RelativeÂ –** When we use consecutive price or quantity.

**P_{1}/P_{0},Â P_{2}/P_{1},Â P_{3}/P_{2}, P_{n}/P_{n-1}**

So, when the above link relative is available with respect to the base period, then we call the relatives as chain relatives. They are in the form:

**P_{1}/P_{0},Â P_{2}/P_{0},Â P_{3}/P_{0}, P_{n}/P_{o}**

## Solved Examples for You!

**Question:Â **From the following data, find out the price index of 1995 using 1990 as a base. Use the simple average price relative method.

Commodity |
A |
B |
C |
D |

Price in Rs. (1990) | 60 | 45 | 80 | 25 |

Price in Rs. (1995) | 75 | 50 | 70 | 40 |

**Solution:Â **

Commodity |
P_{o} |
P_{1} |
P/_{1}P_{0} * 100 |

A | 60 | 75 | 125 |

B | 45 | 50 | 111.11 |

C | 80 | 70 | 87.50 |

D | 25 | 40 | 160.0 |

**âˆ‘ (P _{1}/P_{0} * 100) = 483.61**

**P _{01} =Â **(P

_{1}/P

_{0}* 100)/N = 483.61/4

=Â Rs. 120.9

This concludes our discussion on the topic of index number in statistics.

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