Index Numbers: O Level Statistics 4040 and IGCSE 0479 Study Guide

This guide covers index numbers: Topic 8 of Cambridge O Level Statistics (4040, syllabus for examination in 2025, 2026 and 2027) and Topic 10 of Cambridge IGCSE Statistics (0479, syllabus for examination in 2027). Practise afterwards with the index numbers practice questions.

What the syllabuses ask for

4040 Topic 8 (guidance)	0479 Topic 10 (learning outcomes)
“Including price relatives and weighted aggregate index numbers.”	10.1 Calculate price relatives relative to a base year (price set to 100 for the base year)
	10.2 Understand the meaning of a price relative
“Use and limitations of weighted aggregate index numbers.”	10.3 Calculate a weighted aggregate index number from weights and price relatives; weights come from base-year expenditure and may need to be calculated
	10.4 Interpret and use a weighted aggregate index number
	10.5 Understand the limitations, including the effect of changes in weights caused by changes in consumption

Sources: 4040 syllabus PDF, 0479 syllabus PDF. These are the only two kinds of index number either syllabus names.

1. Price relative

A price relative compares the price of one item in a given year with its price in the base year, with the base-year price set to 100:

price relative = (price in given year ÷ price in base year) × 100

If a bus fare rises from Rs 80 to Rs 92, the price relative is 92 ÷ 80 × 100 = 115. The fare in the given year is 115% of the base-year fare: it has risen by 15%.

A price relative of 100 means no change; below 100 means the price has fallen. The base year’s own price relative is always 100.

You may be asked to work backwards: a price relative of 135 and a current price of Rs 270 give a base-year price of 270 ÷ 135 × 100 = Rs 200.

2. Weighted aggregate index number

One price relative describes one item. To describe the change in the cost of a whole set of items (a family’s shopping, a factory’s raw materials), combine the price relatives in a weighted average, giving more weight to the items people spend more on:

weighted aggregate index = Σ (weight × price relative) ÷ Σ weights

0479 states that the weights come from base-year expenditure. If the question gives prices and quantities rather than weights, calculate each weight as base-year price × base-year quantity.

Worked example

A household’s monthly purchases, with prices in rupees:

Item	Price 2023 (base year)	Price 2025	Quantity bought in 2023
Flour (kg)	120	150	20
Cooking oil (litre)	500	560	6
Milk (litre)	200	230	30
Electricity (unit)	40	52	150

Step 1: price relatives (2023 = 100)

• Flour: 150 ÷ 120 × 100 = 125
• Cooking oil: 560 ÷ 500 × 100 = 112
• Milk: 230 ÷ 200 × 100 = 115
• Electricity: 52 ÷ 40 × 100 = 130

Step 2: weights from base-year expenditure (price × quantity in 2023)

• Flour: 120 × 20 = 2 400
• Cooking oil: 500 × 6 = 3 000
• Milk: 200 × 30 = 6 000
• Electricity: 40 × 150 = 6 000
• Total: 17 400

Step 3: weighted aggregate index

(2 400 × 125 + 3 000 × 112 + 6 000 × 115 + 6 000 × 130) ÷ 17 400 = (300 000 + 336 000 + 690 000 + 780 000) ÷ 17 400 = 2 106 000 ÷ 17 400 = 121.0 (to 1 decimal place)

Interpretation. Taking 2023 as the base year, the cost of this household’s 2023 purchases rose by about 21% by 2025. Electricity and milk dominate the answer, because they carry the largest weights; flour rose by 25% but has the smallest weight.

A check you can do: with weights from base-year expenditure, the index equals (total cost of the 2023 quantities at 2025 prices) ÷ (total cost at 2023 prices) × 100: 21 060 ÷ 17 400 × 100 = 121.0.

3. Interpreting an index number

• An index of 121.0 means prices have risen on average by 21.0% since the base year, weighted by how much was spent on each item.
• It does not mean every item rose by 21%. Here, individual items rose by between 12% and 30%.
• Two indices with the same base year can be compared directly. An index of 121.0 in 2025 and 110.0 in 2024 shows a rise of 11 index points, which is 11 ÷ 110 × 100 = 10% of the 2024 level.

4. Limitations of a weighted aggregate index

• Weights go out of date. Weights are fixed at base-year expenditure. If people change what they buy (0479 names “changes in consumption”), the index no longer reflects actual spending.
• Substitution is ignored. When one item becomes expensive, people often buy less of it and more of a cheaper alternative. A fixed-weight index still counts the old quantity, so it tends to overstate the rise in the cost of living.
• The basket is limited. Only the items chosen are included; new products, and changes in quality, are not captured.
• It is an average. A household whose spending pattern differs from the weights may experience a very different price change.

Where marks are usually lost

• Taking the plain average of the price relatives. In the example above that gives (125 + 112 + 115 + 130) ÷ 4 = 120.5, not 121.0.
• Using given-year quantities, or prices, as weights when the question says weights come from base-year expenditure.
• Writing the price relative “the wrong way up” (base ÷ given): a price rise must give a relative above 100.
• Describing an index of 121 as “prices rose by 121%”.
• Listing limitations in general terms without linking them to the data in the question (for example, “the household may now use less electricity, so its weight is too large”).

Related pages

• Index numbers: practice questions with worked answers
• Crude and standardised rates (4040 Topic 7): another weighted average
• Time series and moving averages (4040 Topic 10)
• Cambridge O Level Statistics 4040 syllabus hub and topic checklist
• Cambridge IGCSE Statistics 0479 syllabus hub