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| \(\blacksquare\) The weightage assigned to an item represents the importance of this item compared to other items involved. |
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| \(\blacksquare\) Weightage can be represented by numbers, ratios, percentages, reading on bar charts or pie charts and others. |
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| \(\blacksquare\) The composite index, \(\bar{I}\), is the average value of all the index numbers with the importance of each item is taken into account. |
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\(\bar{I}=\dfrac{\sum I_iw_i}{\sum w_i}\)
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| where |
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\(I_i=\)index number of the \(i^{th}\) item
\(w_i=\)weightage of the \(i^{th}\) item
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| \(\blacksquare\) For the composite index without the weightage, the weightage for each index number involved is considered to be the same. |
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Example:
Calculate the composite index for the following case.
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| Item |
Price index |
| \(\boldsymbol {A}\) |
\(130\) |
| \(\boldsymbol {B}\) |
\(120\) |
| \(\boldsymbol {C}\) |
\(125\) |
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Based on the question, weightage for each item is \(1\) because the composite indices have no weightage.
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\( \begin{aligned} \bar{I}&=\dfrac{\sum I_iw_i}{\sum w_i} \\\\ &=\dfrac{130(1)+120(1)+125(1)}{3} \\\\ &=\dfrac{375}{3} \\\\ &=125. \end{aligned}\)
