## Composite Index

 10.2 Composite Index
 $$\blacksquare$$ The weightage assigned to an item represents the importance of this item compared to other items involved. $$\blacksquare$$ Weightage can be represented by numbers, ratios, percentages, reading on bar charts or pie charts and others. $$\blacksquare$$ The composite index, $$\bar{I}$$, is the average value of all the index numbers with the importance of each item is taken into account.

$$\bar{I}=\dfrac{\sum I_iw_i}{\sum w_i}$$

 where $$I_i=$$index number of the $$i^{th}$$ item $$w_i=$$weightage of the $$i^{th}$$ item $$\blacksquare$$ For the composite index without the weightage, the weightage for each index number involved is considered to be the same. Example: Calculate the composite index for the following case.
 Item Price index $$\boldsymbol {A}$$ $$130$$ $$\boldsymbol {B}$$ $$120$$ $$\boldsymbol {C}$$ $$125$$
 Based on the question, weightage for each item is $$1$$ because the composite indices have no weightage.

\begin{aligned} \bar{I}&=\dfrac{\sum I_iw_i}{\sum w_i} \\\\ &=\dfrac{130(1)+120(1)+125(1)}{3} \\\\ &=\dfrac{375}{3} \\\\ &=125. \end{aligned}