AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 5
3 marks · Easy difficulty · Reasoning
Evaluate statements comparing two schools' test results based on their mean marks and ranges as True, May be true, or Not true.
Practise this questionQuestion
Question text
5 The table shows information about the marks of students in a test.
Mean mark Range of marks
School A 61 14
School B 56 21
Tick one box for each statement.
[3 marks]
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
Show the mark scheme
Q Answer Mark Comments
True B1 for each
May be true B3
True
5 Additional Guidance
Any unambiguous indication, but if a tick and a cross are used in the same
row, mark the tick
A row with more than one tick is incorrect for that row
How to answer it
Interpreting Statistical Measures: Mean & Range
This question tests your ability to interpret and compare two sets of data using summary statistics:
- Understanding that the mean is a measure of central tendency (average).
- Understanding that the range is a measure of spread (variation/consistency).
- Recognising the limitations of summary statistics (namely, that mean and range give no information about sample size / total frequency).
Question Data Reference
| School | Mean mark | Range of marks |
|---|---|---|
| School A | 61 | 14 |
| School B | 56 | 21 |
"On average, School A had higher marks"
✅ Correct Answer
True
📐 Comparison
- School A mean = 61
- School B mean = 56
- Since 61 > 56, School A’s average is higher.
💡 Key Knowledge
The mean is an average. When a question refers to performance "on average", it is asking you to compare the mean (or median) values. Because 61 is strictly greater than 56, the statement is definitely True.
❌ Common Error
Confusing "on average" with individual marks. A student might think "it might be true because some students in School B could have scored higher than students in School A". But the statement explicitly says "On average", which directly points to the mean.
"There are more students in School B"
✅ Correct Answer
May be true
💡 Key Knowledge
The table only provides summary data: the mean and the range. Neither of these statistics tells us the number of values (sample size / number of students) that went into the calculation.
🧠 Exam Technique
Ask yourself: Can I calculate the number of students from this table? No. School B could have 10 students or 1,000 students. It could have more students than School A, or fewer, or the exact same number. Therefore, it May be true.
❌ Common Error
Assuming that a larger range (21 vs 14) means there must be more students. A larger range only means there is a bigger difference between the highest and lowest mark, not that there are more data points.
"School B had a greater spread of marks"
✅ Correct Answer
True
📐 Comparison
- School A range = 14
- School B range = 21
- Since 21 > 14, School B has a larger range.
💡 Key Knowledge
Range is the standard GCSE measure of spread (or variation). A higher range means the data is more widely spread out (less consistent). School B’s range (21) is greater than School A’s (14), so the spread is definitely greater.
🧠 Examiner Vocabulary
Always link vocabulary terms together in your mind:
- Average / Typical value ↔ Mean / Median / Mode
- Spread / Variation / Consistency ↔ Range (or Interquartile Range)
Summary of Marks & Guidance
📋 Mark Scheme Breakdown (Total: 3 marks)
- Row 1: True [B1]
- Row 2: May be true [B1]
- Row 3: True [B1]
Examiner note: Only tick one box per row. If you change your mind, cross out the incorrect tick clearly. Any row with more than one tick receives 0 marks.
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.