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**CHAIN INDEX NUMBERS**

In the fixed base method which is discussed so far the base remains the same & does not change whole throughout the series. But with the passage of time some items may have been included in the series & other ones might have been deleted, & hence it becomes difficult to compare the result of present conditions with those of the old remote period. Hence the fixed base method does not suit when the conditions change. In such a case the changing base period may be more suitable. Under this method the figures for each year are first expressed as a percentage of the preceding year (called link relatives) then they are chained together by successive multiplication to form a chain index.

**STEPS IN CONSTRUCTION OF CHAIN INDEX**

(1) The figures are to be expressed as the percentage of the preceding year to get link relatives.

Link Relatives of current year =

(2) Chain index is obtained by the formula :

**Example 8:** From the following data find the index numbers by taking (1) 2005 as base (ii) by chain base method.

**Solution Table :** Construction of Index Number taking 2005 as base

This means that from 2005 to 2006 there is an increase of 3.33% (103.33 - 100) from 2005 to 2007 there is an increase of 8.33% (108.33 - 100) increase from 2005 to 2008 there is an increase of 20% (120 - 100) & so on ..........

**Table :** Calculation of Chain Base Index

**Note: **The results obtained by the fixed base & chain base are almost similar. The difference is only due to approximation. Infact the chain base index numbers are always equal to fixed base index numbers if there is only one series.

**Example 9 :**

From the following data compute chain base index number & fixed base index number.

**Solution : Table : **Computation of Chain Base Index Number Calculation of Link Relatives

**Table :** Computation of Fixed base Index No.

**Note : **The two series of index numbers obtained by fixed base & chain base method are different except in the first two years. This would always be so in case of more than one series.

**Example 10 : The price index & quantity index of a commodity were 120 & 110 respectively in 2012 with base 2011. Find its value index number in 2012 with base 2011. Solution :**

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### Chain-Base Index Numbers

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