10.2 Composite Index - SPM Additional Mathematics

10.2 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

\begin{array}{l} \bar{I} = \frac{\sum I W}{\sum W} \\ \bar{I} = \frac{(112) (4) + (104) (3) + (109) (2) + (111) (1)}{4 + 3 + 2 + 1} \\ \bar{I} = \frac{448 + 312 + 218 + 111}{10} \\ \bar{I} = \frac{1089}{10} = 108.9 \end{array}

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:

\begin{array}{l} \bar{I} = \frac{\sum I W}{\sum W} \\ 116.5 = \frac{(110) (4) + (x) (2) + (120) (1) + (115) (3)}{4 + 2 + 1 + 3} \\ 116.5 = \frac{440 + 2 x + 120 + 345}{10} \\ 116.5 = \frac{905 + 2 x}{10} \\ 1165 = 905 + 2 x \\ 2 x = 260 \\ x = 130 \end{array}

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