Weighted Index Calculator
Calculate a weighted composite index number from multiple items with different relative importance weights.
Weighted Index
113.2500
Weighted Index vs Item 1 Index
Formule
## How to Calculate a Weighted Index ### Formula **Weighted Index = Sum(Ii * Wi) / Sum(Wi)** A weighted index combines multiple individual indices using importance weights. This is how composite indices like the CPI are constructed: each component's index is multiplied by its weight (often an expenditure share), then divided by the total weight.
Exemple Résolu
Three items: indices 110, 130, 95 with weights 0.4, 0.35, 0.25.
- 01Weighted sum = 110*0.4 + 130*0.35 + 95*0.25
- 02= 44 + 45.5 + 23.75 = 113.25
- 03Total weight = 0.4 + 0.35 + 0.25 = 1.0
- 04Weighted index = 113.25 / 1.0 = 113.25
- 05Overall prices are 13.25% above the base.
Questions Fréquentes
How are weights determined?
Weights typically reflect relative importance: expenditure shares for price indices, market capitalization for stock indices, or production volumes for output indices. They should sum to 1 (or 100%) but the formula normalizes regardless.
What is the Laspeyres index?
The Laspeyres price index uses base-period quantities as weights: Sum(Pt*Q0)/Sum(P0*Q0). It measures how much a fixed basket costs now versus the base period. CPI is a Laspeyres-type index.
What is the Paasche index?
The Paasche index uses current-period quantities as weights: Sum(Pt*Qt)/Sum(P0*Qt). It measures the cost of the current basket at current vs. base prices. It tends to understate inflation compared to Laspeyres.
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