11.2 Composite Index

11.2 Composite Index




Example 1

Noodle
Price index
Weightage
Fried noodle
112
4
Tomyam noodle
104
3
Seafood noodle
109
2
Wantan noodle
111
1






The above table shows the price indices of a few types of noodles sold at a shop for the year 2000 based on the year 1996 and their respective weightages. Calculate the composite index for the year 2000 based on the year 1996.

Solution:

Composite index for the year 2000 based on the year 1996
I ¯ = I W W I ¯ = ( 112 ) ( 4 ) + ( 104 ) ( 3 ) + ( 109 ) ( 2 ) + ( 111 ) ( 1 ) 4 + 3 + 2 + 1 I ¯ = 448 + 312 + 218 + 111 10 I ¯ = 1089 10 = 108.9


Example 2


Item
Price index
Weightage
P
110
4
Q
x
2
R
120
1
S
115
3






The above table shows the price indices of a few types of items, P, Q, R and S, for the year 2002 based on the year 1997 and their respective weightages. If the composite index for the year 2002 based on the year 1997 is 116.5, find the value of x.

Solution:
I ¯ = I W W 116.5 = ( 110 ) ( 4 ) + ( x ) ( 2 ) + ( 120 ) ( 1 ) + ( 115 ) ( 3 ) 4 + 2 + 1 + 3 116.5 = 440 + 2 x + 120 + 345 10 116.5 = 905 + 2 x 10 1165 = 905 + 2 x 2 x = 260 x = 130

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