Composite index numbers measure changes in the prices of many goods aggregated into one index number. Univariate index numbers measure changes in a single variable. Chain index numbers use a changing base year, where the previous year serves as the base for the current year. Index numbers provide relative changes but have limitations like not accounting for qualitative changes, potential errors, and lack of perfect accuracy.

1. Index Number

2. Index Numbers
• Composite Index Number
• Univariate Index Number
• Fixed Index Number
• Chain Index Number

3. Composite Index Number
• A composite index number measures the variation in the value of a
composite number defined as the aggregate of a set of elementary
numbers (for example, the consumer price index measures the
variation in the prices of 1,000 varieties of products in a single
index number).
• When index number is calculated by using group of variable, it is
called Composite Index Number.

5. Univariate Index Number
• When index number is calculated from a single variable, it is
called Univariate Index Number
• The construction univariate index number is a simple idea.

6. Price Index Number
• Price index numbers measure the relative changes in the price of a
commodity between two periods. Prices can be either retail or
wholesale.

7. Quantity Index Numbers
• These index numbers are considered to measure changes in the
physical quantity of goods produced, consumed or sold for an item
or a group of items.

8. Chain Base Index Number
When this method is used the comparisons are not made with a
fixed base, rather the base changes from year to year. For example,
for 2007,2006 will be the base; for 2006, 2005 will be the same and
so on.
Chain Index for Current Year:
= Average link relative of current year x Chain index of previous year
100

9. EXAMPLE-
• From the Data given Below construct an index number by chain
base method.
• Price of a commodity from 2006 to 2008.

10. Solution-

11. Limitations:
• Provides relative changes only
• Lack of Perfect Accuracy
• Difference between purpose and method of construction
• Ignores qualitative changes
• Manipulations are possible
• There may be errors in the choice of base periods or weights.
• Comparisons of changes in variables over long periods are not reliable
• They are not capable of being used for any other purpose than the one
for which they have been constructed particularly.