Index Numbers
Index numbers measure changes in a quantity relative to a base year and are used to build composite indices with weightages. SPM tests price and quantity indices, the interpretation of index values, and weighted composite indices.
Core rules
Index number I = (Q₁/Q₀) × 100, where Q₀ is the base-year value and Q₁ the current value. A composite index is Ī = Σ(IᵢWᵢ)/ΣWᵢ, where the Wᵢ are weightages, often quantities. Index numbers carry no units; they express relative change, so I = 125 means a 25% increase from the base year.
Worked example
Two items have price indices 120 and 150 with weightages 3 and 2. Composite index = (120×3 + 150×2)/(3 + 2) = (360 + 300)/5 = 660/5 = 132. Overall, prices rose by 32% relative to the base year.
Traps
Taking a simple average instead of the weighted formula; dividing by the wrong total weight; reading an index as a percentage change rather than a level; mixing values from different base years.