Composite Index

Composite Index

10.2

Composite Index

The image is an infographic titled ‘COMPOSITE INDEX’ by Pandai. It contains three star-shaped text boxes with the following information: 1. Top left box: ‘The weightage assigned to an item represents the importance of this item compared to other items involved.’ 2. Top right box: ‘Weightage can be represented by numbers, ratios, percentages, reading on bar charts or pie charts and others.’ 3. Bottom right box: ‘For the composite index without the weightage, the weightage for each index number involved is considered to be the same.’ The design features a clean layout with a focus on explaining the concept of composite index and weightage.

Formula

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 \(i^\text{th}\) item,
\(w_i=\) weightage of the \(i^\text{th}\) item.

Example

Question

Calculate the composite index for the following case.

Item	Price Index
\(A\)	\(130\)
\(B\)	\(120\)
\(C\)	\(125\)

Solution

Based on the question, weightage for each item is \(1\) because the composite indices have no weightage.

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

Composite Index

10.2

Composite Index

The image is an infographic titled ‘COMPOSITE INDEX’ by Pandai. It contains three star-shaped text boxes with the following information: 1. Top left box: ‘The weightage assigned to an item represents the importance of this item compared to other items involved.’ 2. Top right box: ‘Weightage can be represented by numbers, ratios, percentages, reading on bar charts or pie charts and others.’ 3. Bottom right box: ‘For the composite index without the weightage, the weightage for each index number involved is considered to be the same.’ The design features a clean layout with a focus on explaining the concept of composite index and weightage.

Formula

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 \(i^\text{th}\) item,
\(w_i=\) weightage of the \(i^\text{th}\) item.

Example

Question

Calculate the composite index for the following case.

Item	Price Index
\(A\)	\(130\)
\(B\)	\(120\)
\(C\)	\(125\)

Solution

Based on the question, weightage for each item is \(1\) because the composite indices have no weightage.

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