AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 19
3 marks · Easy difficulty · Reasoning
Use the mean and range from a summary table to evaluate three statements comparing the test marks of two schools as True, May be true, or Not true.
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Mark scheme
Show the mark scheme
How to answer it
Comparing Distributions: Mean and Range
AQA GCSE Mathematics • Statistics • 3 Marks
What this question tests
This question evaluates your ability to interpret statistical measures from a summary table and assess the validity of comparative statements:
- Understanding that the mean is a measure of average / central tendency.
- Understanding that the range is a measure of spread / dispersion / consistency.
- Distinguishing between facts guaranteed by summary statistics and unknown information (e.g. sample size / total student counts).
Question Data Provided
| Mean mark | Range of marks | |
|---|---|---|
| School A | 61 | 14 |
| School B | 56 | 21 |
Statement Analysis & Correct Answers
| Statement | True | May be true | Not true |
|---|---|---|---|
| On average, School A had higher marks | ✓ | ||
| There are more students in School B | ✓ | ||
| School B had a greater spread of marks | ✓ |
Mark Scheme Breakdown:
• Row 1: True [B1]
• Row 2: May be true [B1]
• Row 3: True [B1]
Total: 3 marks (Independent B marks).
• Row 1: True [B1]
• Row 2: May be true [B1]
• Row 3: True [B1]
Total: 3 marks (Independent B marks).
Statement 1: "On average, School A had higher marks"
Correct Box: True
- Why: The mean is a formal measure of average.
- School A mean = 61
- School B mean = 56
- Since 61 > 56 , it is definitely True that School A had higher marks on average.
Statement 2: "There are more students in School B"
Correct Box: May be true
- Why: The table only reports the mean and the range. Neither metric reveals the sample size (number of students n ).
- School B might have 30 students while School A has 100, or vice versa.
- Because we do not have frequency data, it could be true or it could be false → May be true.
Statement 3: "School B had a greater spread of marks"
Correct Box: True
- Why: Range measures the spread of the data ( highest mark − lowest mark ).
- School A range = 14
- School B range = 21
- Since 21 > 14 , School B definitely had a greater spread (its marks were less consistent) → True.
🧠 Exam Technique & Vocabulary Pairs
- Always link statistical terms to their everyday descriptions:
- Average / Typical value ↔ Mean or Median
- Spread / Variation / Consistency ↔ Range or Interquartile Range (IQR)
- A smaller range means data values are more consistent and closer together.
- A larger range means data values are more spread out and less consistent.
❌ Common Student Pitfalls
- Ticking multiple boxes: The mark scheme explicitly states that any row with more than one tick gets 0 marks for that row.
- Assuming larger range = more students: Confusing the spread of values with the frequency of students. School B could have just 2 students scoring 0 and 21 (range = 21).
- Selecting "Not true" for statement 2: Students often think "I cannot prove it, so it must be false". If it is possible, choose May be true.
Examiner Notes & Marking Rules
- Ambiguous marks: If both a tick and a cross are placed in the same row, examiners are instructed to mark the tick.
- Clean entries: If you change your mind, completely cross out the wrong box rather than leaving two partial ticks.
Topics
Statistics · 3.6 Statistics
Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.