Composite Index


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.

\(\bar{I}=\dfrac{\sum I_iw_i}{\sum w_i}\)


\(I_i=\)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.


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.


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