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Class 11 Index Numbers: cheat sheet
CBSE Social Science. Measuring relative change over time: price relatives, simple and weighted indices, Laspeyres and Paasche, CPI, WPI, IIP and the Sensex, real wages and inflation.
Key ideas
- An index number measures the relative change in a group of items between a base period (taken as 100) and a current period.
- A good base year is normal, without extreme values, and not too far in the past.
- A simple aggregative index treats all items as equally important; a weighted index weights them by importance.
- Laspeyres weights prices by base period quantities and Paasche by current period quantities; only the weights differ.
- The CPI (cost of living index) tracks retail prices for a group of consumers; the WPI tracks wholesale prices of goods; the IIP tracks industrial output; the Sensex tracks the shares of 30 companies.
- When prices rise, the purchasing power of money falls, so wages must be adjusted to keep the same standard of living.
Remember
| Price relative | p₁ ÷ p₀ × 100 |
| Simple aggregative | Σp₁ ÷ Σp₀ × 100 |
| Laspeyres | Σp₁q₀ ÷ Σp₀q₀ × 100 |
| Paasche | Σp₁q₁ ÷ Σp₀q₁ × 100 |
| Weighted index of relatives | ΣWR ÷ ΣW |
| Real wage | money wage ÷ CPI × 100 |
| Salary to keep up | base salary × CPI ÷ 100 |
| Inflation rate | (new index − old index) ÷ old index × 100 |
| IIP weights (book) | mining 14.4, manufacturing 77.6, electricity 8.0 (base 2011–12) |
Watch out
- Dividing the base price by the current price (the current price goes on top).
- Swapping the weights: Laspeyres uses q₀, Paasche uses q₁.
- Finding inflation by dividing by the new index instead of the old one.
Worked example
Find the price index by the simple average of price relatives: sugar ₹18 → ₹24, oil ₹23 → ₹22, milk ₹16 → ₹16, tea ₹10 → ₹12.
Working: relatives 133.33, 95.65, 100, 120; their mean
Answer: 112.25
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