STATISTICS ASSIGNMENT-I
What methods of Index Number calculation is used to calculate Cost of Living Index ?
Introduction:
An INDEX NUMBER measures the relative change in price, quantity, value, or some other item of interest from one time period to another. Classification of index numbers:
According to purpose for which index numbers are used are classified as below.
i) Price index number ii) Quality index number iii) Value index number iv) Special purpose index number
Price index number: Price index number measures the changes in the price level of one commodity or group of commodities between two points of time or two areas.
Ex: Wholesale price index numbers, Retail price index numbers, Consumer price index numbers.

Quantity index number: Quantity index numbers measures the changes in the volume of production, sales, etc in different sectors of economy with respect to time period or space.
Note: Price and Quantity index numbers are called market index numbers.
Methods of constructing index numbers: A large number of formulae have been derived for constructing index numbers. They can be
1) Unweighted indices
a) Simple aggregative method
b) Simple average of relatives.
2) Weighted indices
a) Weighted aggregative method b) Weighted average of relatives
Weighted index is preferred over unweighted index as rational weights are assigned to various items in explicit fashion. Below are the different
i. Laspeyres method: It is the most important of all the types of index numbers. In this method the base year quantities are taken weights. The formula for constructing Laspeyres price index number P01La=
P0 are the base year prices, P1 are the current year prices, P01 is the price index number for the current year with reference to the base year, q0 is the quantity sold in the base period

ii. Paasche method: In this method the current year quantities are taken as weights and the formula is given by
P01Pa=
q1 is the quantity sold each year that the index is computed.

iii. Fisher’s ideal method: Fishers price index number is given by the G.M of the Laspeyres and Paasche index numbers. P01F= iv. Dorbey’s and Bowley’s method
Dorbey’s and Bowley’s price index number is given by the A.M of the Laspeyres and Paasche index numbers.
P01DB=
The Fisher’s index number is called ‘ideal index number’ due to the following characteristics.
1) It is based on the G.M which is theoretically considered as the best average of constructing index numbers.
2) It takes into account both current and base year prices as quantities.

COST OF LIVING INDEX NUMBERS (or) CONSUMER PRICE INDEX NUMBERS:

The cost of living index measures the changes in the level of prices of commodities which directly affects the cost of living of a specified group of persons at a specified place. The general index numbers fails to give an idea on cost of living of different classes of people at different places. As mentioned earlier, this is one of the price indices.

Methods for construction of cost of living index numbers:
Cost of living index number can be constructed by the following formulae. 1) Aggregate expenditure method or weighted aggregative method
2) Family budget method or the method of weighted relatives

1) Aggregate expenditure method or weighted aggregative method
In this method the quantities of commodities consumed by the particular group in the base year are taken as weights. The formula is given by Cost of living index =

2) Family budget method or the method of weighted relatives In this method cost of living index is obtained on taking the weighted average of price relatives, the weights are the values of quantities consumed in the base year i.e. . Thus the consumer price index number is given by Cost of living index =
Where for each item , value on the base year

Note: It should be noted that the answer obtained by applying the aggregate expenditure method and family budget method shall be same. However, aggregate expenditure method is preferred because it is far easier to apply compared to the family budget method.