AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 4

2 marks · Medium difficulty · Short Answer

Work out the inter-quartile range of a given set of 11 ordered numbers.

Practise this question

Question

Question 4 states: 'Here are 11 numbers.' followed by a list: 2, 8, 10, 12, 12, 14, 19, 23, 26, 31, 33. Below the numbers, it asks to 'Work out the inter-quartile range.' with lines for working and an answer line, worth 2 marks.
Question text

4 Here are 11 numbers.

28 10 12 12 14 19 23 26 31 33

Work out the inter-quartile range.

[2 marks]

Answer

Mark scheme

Show the mark scheme Mark scheme table for Question 4 showing M1 for '10 or 26 used' and A1 for the answer '16'. Additional guidance specifies that obtaining 10 from 12 - 2 or 33 - 23 does not score M1.

Q Answer Mark Comments

10 or 26 used M1

16 A1

Additional Guidance

10 from 12 – 2 or 33 – 23 does not score M1

How to answer it

Interquartile Range from an Ordered List

📌 What this question tests

This question tests your ability to find the lower quartile (Q₁) and upper quartile (Q₃) from a small, discrete data set and use them to calculate the interquartile range (IQR).

Question 4 • 2 Marks

Finding the Interquartile Range

Data: 2, 8, 10, 12, 12, 14, 19, 23, 26, 31, 33

2
8
10 (Q₁)
12
12
14 (Median)
19
23
26 (Q₃)
31
33

📐 Step-by-Step Calculation

  1. Check the order: The 11 values are already arranged in ascending order.
  2. Find the median (middle value):
    Position = (11 + 1) ÷ 2 = 6th value.
    The 6th value is 14 .
  3. Find the Lower Quartile (Q₁):
    Look at the 5 numbers below the median: 2, 8, 10, 12, 12 .
    The middle of this lower half is the 3rd value: 10.
  4. Find the Upper Quartile (Q₃):
    Look at the 5 numbers above the median: 19, 23, 26, 31, 33 .
    The middle of this upper half is the 9th value: 26.
  5. Calculate IQR:
    IQR = Q₃ − Q₁ = 26 − 10 = 16.

✅ Mark Scheme Breakdown

  • Method Mark [M1]: Identifying and using either 10 (lower quartile) or 26 (upper quartile).
  • Accuracy Mark [A1]: Correct final answer of 16.
Examiner Note: A calculation giving 10 accidentally (e.g. 12 − 2 = 10 or 33 − 23 = 10) does not gain the M1 mark. It must clearly be used as the lower quartile.

💡 Key Knowledge

  • Range: Maximum value − Minimum value (measures overall spread).
  • Interquartile Range (IQR): Upper Quartile − Lower Quartile (measures the spread of the middle 50% of the data).
  • Quartile Positions: For n = 11 :
    • Median position = (11 + 1) / 2 = 6th
    • Lower quartile = middle of lower 5 values = 3rd
    • Upper quartile = middle of upper 5 values = 9th

🧠 Exam Technique

  • Always show your working: Clearly state LQ = 10 and UQ = 26 before subtracting. If you make an arithmetic slip, stating the quartiles guarantees you score M1 !
  • Circle values directly: Circle the median first, then box the lower and upper quartiles on the question paper to avoid miscounting.

❌ Common Errors

  • Calculating full range: Subtracting lowest from highest ( 33 − 2 = 31 ) instead of using the quartiles.
  • Including the median: Incorrectly including the median ( 14 ) when finding the median of the halves.
  • Giving a pair instead of a difference: Leaving the answer as 10 to 26 rather than evaluating the subtraction.

Topics

Statistics · 3.6 Statistics

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.