Index Numbers: O Level Statistics 4040 and IGCSE 0479 Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs. Use them alongside the official past papers from Cambridge.

Study the method first: index numbers study guide.

---

Questions

1. The price of a bus ticket rose from Rs 80 in 2023 to Rs 92 in 2025. Using 2023 as the base year, calculate the price relative for 2025. [1]

2. The price relative of a textbook in 2025, with 2022 as the base year, is 135. The textbook costs Rs 270 in 2025. Find its price in 2022. [2]

3. A cost-of-living index for a city uses four groups of spending. The weights and the 2025 price relatives (2020 = 100) are:

Group	Weight	Price relative
Food	45	118
Housing	30	106
Transport	15	124
Other	10	110

(a) Calculate the weighted aggregate index for 2025. [3]

(b) Interpret your answer. [1]

(c) Transport has the highest price relative, but changes to it affect the index less than changes to food. Explain why. [1]

4. A bakery buys three ingredients. Its prices (Rs per kg) and the quantities it used in the base year, 2024, are:

Ingredient	Price 2024	Price 2025	Quantity used in 2024 (kg)
Flour	60	75	40
Butter	250	270	8
Sugar	30	36	50

(a) Calculate the price relative for each ingredient, using 2024 as the base year. [2]

(b) Calculate a weight for each ingredient from base-year expenditure. [2]

(c) Calculate the weighted aggregate index for 2025. [3]

5. By 2025 the bakery in Question 4 uses much less butter and more margarine, which is not in the index. Give two reasons why the index in 4(c) may no longer measure the change in the bakery’s costs accurately. [2]

---

Answers

1. 92 ÷ 80 × 100 = 115 [1].

2. Price in 2022 = 270 ÷ 135 × 100 [1] = Rs 200 [1].

3. (a) 45 × 118 + 30 × 106 + 15 × 124 + 10 × 110 = 5 310 + 3 180 + 1 860 + 1 100 = 11 450 [1]; sum of weights = 100 [1]; index = 11 450 ÷ 100 = 114.5 [1].

(b) On average, weighted by spending, prices in the city rose by 14.5% between 2020 and 2025 [1].

(c) Food has a weight of 45 against 15 for transport, so a one-point change in the food price relative moves the index three times as much [1].

4. (a) Flour 75 ÷ 60 × 100 = 125; butter 270 ÷ 250 × 100 = 108; sugar 36 ÷ 30 × 100 = 120 [2] (1 mark for two correct).

(b) Flour 60 × 40 = 2 400; butter 250 × 8 = 2 000; sugar 30 × 50 = 1 500 [2] (1 mark for two correct). Total 5 900.

(c) (2 400 × 125 + 2 000 × 108 + 1 500 × 120) ÷ 5 900 [1] = (300 000 + 216 000 + 180 000) ÷ 5 900 = 696 000 ÷ 5 900 [1] = 118.0 (to 1 decimal place) [1].

5. Any two, linked to the bakery:

• The weights are based on 2024 spending; the bakery now buys less butter, so butter’s weight is too large [1].
• Margarine is now part of the bakery’s costs but is not in the index at all [1].
• The index assumes the same quantities are bought each year, so it does not reflect the bakery switching to a cheaper ingredient [1].

---

Where marks are usually lost

• Averaging price relatives without weights: in 4(c) that gives (125 + 108 + 120) ÷ 3 = 117.7, not 118.0.
• Using the quantities (40, 8, 50) as the weights instead of base-year expenditure (price × quantity).
• Dividing by the number of items instead of by the sum of the weights.
• In 3(b), saying prices rose by 114.5%.
• In Question 5, writing general limitations (“weights change”) without saying which weight and why.

Next steps

• Crude and standardised rates practice
• Time series practice
• O Level Statistics 4040 hub · IGCSE Statistics 0479 hub