AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 13

4 marks · Medium difficulty · Multi-step Problem

Calculate the range of mobile phone usage over four weeks, and determine the usage in a fifth week given the overall mean for all five weeks.

Practise this question

Question

Question 13 introduces a dataset: 'Ingrid records the number of minutes she uses her mobile phone over four weeks: 140, 168, 205, 192.' Part (a) asks to work out the range, worth 1 mark. Part (b) states that Ingrid records the minutes for a fifth week and the mean for all five weeks is 178 minutes, then asks to work out the number of minutes used in the fifth week, worth 3 marks.

Mark scheme

Show the mark scheme Mark scheme for question 13. For part (a), the answer is 65, awarded B1. For part (b), multiple methods are provided. Method 1 (works with total): M1 for 178 * 5 or 890, or setting up (140 + 168 + 205 + 192 + x) / 5 = 178; M1dep for 890 - 705; A1 for 185. Alternative methods include using differences from the mean, working from the mean of the 4 given values, trial and improvement, and numerical solutions.

How to answer it

Calculating the Range and Working Backwards from a Mean

What This Question Tests

This question assesses your ability to interpret and work with core statistical measures:

  • Range: Identifying extreme values in a small data set and calculating the measure of spread.
  • Reverse Mean Problem: Reconstructing the total sum from a known mean and number of values ( Total = Mean × n ), then finding a missing value.
Question 13 (a) • 1 Mark

Part (a): Finding the Range

Data values: 140, 168, 205, 192

📐 Step-by-Step Calculation

  1. Find the highest value: 205
  2. Find the lowest value: 140
  3. Subtract lowest from highest:
    205 − 140 = 65

✅ Correct Answer

65 minutes

Mark Scheme: B1 for fully correct value of 65.

💡 Key Knowledge

  • Range = Highest Value − Lowest Value
  • Range is a single number showing the spread of data, not an average.

❌ Common Errors

  • Writing the range as an interval (e.g. 140 to 205 or 140 − 205 ) instead of computing the difference.
  • Accidentally picking 192 instead of 205 as the largest value.
Question 13 (b) • 3 Marks

Part (b): Finding the Missing Fifth Week

A fifth week is added. Mean for all five weeks = 178 minutes.

📐 Step-by-Step Method (Standard Method)

  1. Find the target total for all 5 weeks:
    Total = Mean × Number of values = 178 × 5 = 890
  2. Find the sum of the first 4 weeks:
    140 + 168 + 205 + 192 = 705
  3. Subtract the known total from the required total:
    890 − 705 = 185 minutes

✅ Correct Answer

185 minutes

Mark Breakdown:
  • M1: 178 × 5 (or 890 ) OR setting up an equation: (705 + x) ÷ 5 = 178
  • M1dep: Complete method: 890 − 705
  • A1: Correct answer of 185

🧠 Exam Technique & Alternative Methods

  • The "Total First" Rule: Whenever an exam question states the mean and the count, multiply them immediately to find the total sum.
  • Difference from Mean Method: Look at how far the 4 known values deviate from 178:
    (140 − 178) = −38
    (168 − 178) = −10
    (205 − 178) = +27
    (192 − 178) = +14
    Total deviation = −7. Therefore, the 5th value must be 7 above the mean: 178 + 7 = 185 .

❌ Common Errors & Traps

  • Dividing by 4 instead of 5: Forgetting that Ingrid now records data for five weeks in total.
  • Adding 178 to the list: Confusing the new mean with the value of the fifth week itself.
  • Time Conversion Pitfall: The answer line specifies "minutes". If converted to hours, write 3 hours 5 minutes (giving 3.08 hours or 3.05 hours will lose marks; the mark scheme allows a special case SC2 for exactly 3 hrs 5 mins ). Keep it simple and leave it as 185 .

💡 Examiner Commentary

Students who set up an algebraic equation (705 + x) ÷ 5 = 178 or clearly found 178 × 5 = 890 scored method marks easily even if they made a final subtraction slip. Always show the multiplication step explicitly on your paper.

Topics

Statistics · Number · 3.6 Statistics · 3.1.1 Structure and calculation

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.