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

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