Calculate and interpret index numbers
Compare prices with a base year, construct weighted aggregate indices and explain what the index does and does not represent.
Section Paper 1 · Written · calculator required
Exam scope and assessment notes
This lesson maps the Calculate and interpret index numbers section of Cambridge IGCSE Statistics 0479 (2027 and 2028–2030 syllabus versions). This is original StudyForA teaching and self-check practice, not Cambridge material, an official mark scheme, a timed mock or an official grade. Charts and written working are not automatically assessed; human subject-teacher review remains pending. Use the syllabus version for your exam year. Cambridge offers 0479 in the June series only and does not make it available in every administrative zone. Check the current Cambridge 0479 page and confirm your centre's entry eligibility with your exams officer.
Before you begin
- Use the earlier 0479 ideas where needed; write units, working and a contextual interpretation for each result.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is 15% more than a base value of 200?
What you will learn
- Calculate price relatives against a base year set to 100
- Interpret a price relative
- Calculate a weighted aggregate index using base-year expenditure weights
- Interpret an aggregate index and assess its limits and changing weights
A price relative compares one item with its base price
Price relative = current price ÷ base-year price × 100. The base-year relative is 100. A value of 125 means the price is 25% above the base-year price; it does not mean the item costs 125 currency units.
Weights reflect base-year expenditure
A weighted aggregate index combines price relatives using weights based on expenditure in the base year. If weights are not given, base-year quantity × base-year price can provide each expenditure weight. Weighted index = Σ(weight × relative) ÷ Σweights.
A larger weight gives an item greater influence. The index summarises the chosen basket; it may not match every household's experience.
Consumption and method create limitations
The index depends on the chosen goods, base year, prices and weights. Consumption patterns may change, making old weights less representative. Quality, substitutions and differences between consumers may not be captured. State the basket and period when interpreting the result.
Pause and explain
Why might an old weighted index become less representative?
Worked example
A basket costs $80 in the base year and $92 now. Find its price relative and interpret it.
Show the worked solution
- Relative = 92/80 × 100.
- 92/80 = 1.15.
- 1.15 × 100 = 115.
Answer The price relative is 115, so the basket's price is 15% higher than in the base year.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A product costs $24 in the base year and $30 now. Find its price relative and percentage change.
Give me a hint
Divide current price by base price, multiply by 100, then compare with 100.
Compare my reasoning
- Relative = 30/24×100 = 125.
- Percentage increase = 125 − 100 = 25%.
- An index point value and a currency price are different quantities.
Price relative 125; the price has increased by 25% from the base year.
Look for these in your work
- Relative formula correct
- Percentage change correct
- Interpretation distinguishes index from price
Two items have price relatives 120 and 90 with base-year expenditure weights 300 and 700. Find the weighted aggregate index.
Give me a hint
Calculate the weighted total and divide by total weight.
Compare my reasoning
- Weighted total = 120×300 + 90×700 = 99 000.
- Total weight = 1000.
- Index = 99 000/1000 = 99.
The weighted aggregate index is 99, indicating that the weighted basket is 1% below its base-year level under these weights.
Look for these in your work
- Weights paired with correct relatives
- Weighted mean correct
- Interpretation correct
A family now spends a much larger share of its budget on internet access than it did in the base year. Explain why an index using old weights may misstate its experience.
Give me a hint
Index weights represent the chosen base-year basket, not every current household.
Compare my reasoning
- The index gives internet access its old base-year weight.
- The family's current expenditure pattern is different.
- A revised basket or separate household-specific index may better describe its costs, but uses a different basis.
Old weights may understate the influence of internet costs for this family because its spending pattern changed. The index still describes the specified base-year basket; it is not necessarily the family's personal inflation rate.
Look for these in your work
- Old weight effect stated
- Context connected
- Index scope qualified
Common mistakes
- Subtracting prices instead of calculating a relative
- Using current expenditure as the specified base-year weight
- Describing an index of 115 as a price of 115
- Ignoring how consumption changes can make weights less representative
What can you explain now?
A price relative is 92. How does the current price compare with the base-year price?
Compare with the explanation
It is 8% below the base-year price
An index of 100 represents the base; 92 is 8 index points lower.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
What does a weighted aggregate index of 112 mean, and what determines each item's influence?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.