Why a composite index?
A single price index describes one item only. A composite index combines several individual indices into one figure, using a weightage for each to show its relative importance. The result is a weighted mean of the individual indices.
Key formula
Composite index: Ī = Σ(Iᵢ wᵢ) / Σ wᵢ, where Iᵢ is each item's index and wᵢ its weightage.
Applying weightages
Multiply each index by its weight, add the products, then divide by the total of the weights. Weights may be given as ratios, quantities, or percentages.
Worked example
Three items have indices 110, 120, and 130 with weightages 2, 3, and 5. Find the composite index. Numerator = 110×2 + 120×3 + 130×5 = 220 + 360 + 650 = 1230. Sum of weights = 2 + 3 + 5 = 10. Ī = 1230 / 10 = 123. So overall prices rose 23% relative to the base.
Working with weights
Weights show how important each item is in the whole. They may be given as raw quantities, ratios, or percentages, and the formula works the same way in each case because dividing by Σw normalises them. If a household spends more on food than on clothing, food carries a larger weight and moves the composite index more. To find a later total cost, multiply the base cost by the composite index and divide by 100: if a basket cost RM500 at the base and the composite index is 123, the new cost is 500 × 123/100 = RM615. This is why the composite index is widely used to track the overall cost of living.
Remember
- Composite index = weighted mean of individual indices.
- Divide by the SUM of the weights, not the count.
- Larger weight = greater influence on the result.