OxfordAQA International GCSE Mathematics: Interpreting graphs, comparing distributions and correlation (9260) – 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 – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions are for OxfordAQA International GCSE Mathematics (9260), specification Version 5.1 (for exams May/June 2018 onwards), section 3.4.2 Interpretation, references S6, S7 and S8. All of it is Core content, so it can also appear on the Extension papers. Nothing is Extension only. The links to the guide, notes, hub, checklist and diagnostics are in Next steps.

Questions

1. A library recorded 300 loans in one week. A pie chart of the loans has these angles: fiction 144°, non-fiction 90°, comics 66°, magazines 60°.

(a) Work out the number of fiction loans. [2] (b) How many more non-fiction loans than magazine loans were there? [2]

2. A dual bar chart shows the number of members of a sports club in two years, by age group.

Age group	2024	2025
Under 12	35	42
12 to 17	48	45
18 to 29	30	36
30 and over	22	27

(a) Find the total membership in each year. [2] (b) Work out the percentage increase in total membership, to 1 decimal place. [2]

3. A bar chart compares the annual profit of two companies: A made £52 million and B made £56 million. The vertical axis of the chart starts at £50 million.

(a) Explain why the chart is misleading. [1] (b) How many times taller than A’s bar does B’s bar appear? [1] (c) Work out B’s actual profit as a percentage of A’s, to 1 decimal place. [1]

4. A line graph shows the number of cars in a car park at the start of each hour. The points are joined with straight lines.

Time	08:00	09:00	10:00	11:00	12:00	13:00	14:00
Cars	40	85	120	135	150	110	70

(a) In which hour was the increase greatest, and what was it? [1] (b) The car park holds 140 cars. Estimate the time at which it first became full. [2] (c) The manager says there will be 30 cars at 15:00 because the fall continues at the same rate. Comment. [1]

5. The battery life, in hours, of eight tests of each of two phone models is recorded.

Model P: 14, 15, 15, 16, 17, 18, 18, 19
Model Q: 12, 13, 16, 17, 17, 19, 20, 22

(a) Find the mean for each model. [2] (b) Find the range for each model. [2] (c) Compare the two models, using your answers. [2]

6. Waiting times at two clinics were recorded for 50 patients each.

Waiting time, t (minutes)	Clinic A	Clinic B
0 < t ≤ 10	5	12
10 < t ≤ 20	14	20
20 < t ≤ 30	18	10
30 < t ≤ 40	9	6
40 < t ≤ 50	4	2

(a) Estimate the mean waiting time at each clinic. [4] (b) Compare the waiting times at the two clinics, using the modal classes and your answer to part (a). [2]

7. The heights of 9 seedlings grown without fertiliser and 9 grown with fertiliser were measured in cm.

    Without                | Stem |     With
           8   7   5   2   |  1   |  8
       9   6   4   3   1   |  2   |  1  2  4  5  7  8
                           |  3   |  1  3

Key: for the “without” group 4 | 2 means 24 cm. For the “with” group 2 | 4 means 24 cm.

(a) Find the median height for each group. [2] (b) Find the range for each group. [2] (c) Does the fertiliser help growth? Give a conclusion and one reason for caution. [2]

8. State the correlation you would expect (positive, negative or none, and weak or strong where it applies).

(a) The age of a child (3 to 12 years) and the child’s height. [1] (b) The height above sea level of a mountain town and its average temperature. [1] (c) A pupil’s house number and their test mark. [1]

9. Monthly sales of sun cream and of ice lollies in a seaside shop show strong positive correlation. A shop assistant says that buying sun cream makes customers want lollies.

(a) Describe the correlation. [1] (b) Explain why the assistant’s claim is not justified by the data. [1] (c) Suggest another factor that could explain the correlation. [1]

10. A kiosk records the midday temperature in °C (x) and the number of hot drinks sold that day, in hundreds (y), on ten days.

x	1	2	3	3	4	5	6	7	8	9
y	14.8	13.1	12.4	11.9	10.6	9.2	8.7	7.1	6.4	5.0

(a) Describe the correlation. [1] (b) Work out the mean point (x̄, ȳ). [2] (c) Dev draws a line of best fit by eye through (1, 14.4) and (9, 5.2). Show that the line passes close to the mean point. [1] (d) Find the equation of Dev’s line in the form y = mx + c. [3] (e) Use the line to estimate the drinks sold on a day when the temperature is 6.5 °C. [1] (f) Explain what the gradient means in this context. [1] (g) Say why the line is unsuitable for a day at 20 °C. [1]

11. A teacher records hours of sleep (x) and reaction time in milliseconds (y) for nine pupils.

x	5	5.5	6	6.5	7	7.5	8	8.5	9
y	342	331	322	305	296	284	330	262	251

(a) One pupil does not follow the trend. Identify the pupil and give a reason for your choice. [2] (b) Ignoring that pupil, find the mean point for the other eight. [2] (c) A line of best fit passes through (5, 342) and (9, 250). Find its equation. [3] (d) Estimate the reaction time after 7.2 hours of sleep. [1] (e) Estimate the reaction time after 10 hours of sleep and comment on its reliability. [2]

Answers

1. (a) Fraction = 144/360 [1]. Loans = 144/360 × 300 = 120 [1] [2] (b) Non-fiction = 90/360 × 300 = 75 and magazines = 60/360 × 300 = 50 [1]. Difference = 75 - 50 = 25 [1] [2] Examiner insight: Convert angles to numbers of loans before subtracting. A difference of angles (30°) answers a different question.

2. (a) 2024: 35 + 48 + 30 + 22 = 135 [1]. 2025: 42 + 45 + 36 + 27 = 150 [1] [2] (b) Increase = 150 - 135 = 15 [1]. 15/135 × 100 = 11.1% [1] [2] Examiner insight: Divide a percentage change by the starting value. Dividing 15 by 150 gives 10.0%, a common slip.

3. (a) The vertical axis starts at £50 million, not 0, so the bars exaggerate the difference [1] [1] (b) Visible heights are 6 and 2, so B looks 3 times as tall [1] [1] (c) 56/52 × 100 = 107.7% [1] [1] Examiner insight: Say what is wrong with the scale, not only “it is misleading”. Linking the 3 times effect to the true ratio makes it specific.

4. (a) Between 08:00 and 09:00, an increase of 45 cars [1] [1] (b) From 135 at 11:00 the line rises 15 in the hour, so 5 more cars takes 5/15 hour = 20 minutes [1]. Full at about 11:20 [1] [2] (c) The fall of 40 an hour would give 30, but the graph ends at 14:00, so this extrapolation is unreliable [1] [1] Examiner insight: State the steady-change assumption behind an estimate between readings. Predictions beyond the last reading need a comment on reliability.

5. (a) P: 132 ÷ 8 = 16.5 hours [1]. Q: 136 ÷ 8 = 17 hours [1] [2] (b) P: 19 - 14 = 5 [1]. Q: 22 - 12 = 10 [1] [2] (c) Q has a slightly higher mean (17 against 16.5) [1], but P is more consistent because its range is smaller (5 against 10) [1] [2] Examiner insight: A strong comparison quotes an average and a spread for both sets and concludes in context.

6. (a) Midpoints 5, 15, 25, 35, 45. A: 5(5) + 14(15) + 18(25) + 9(35) + 4(45) = 25 + 210 + 450 + 315 + 180 = 1180 [1]. 1180 ÷ 50 = 23.6 minutes [1]. B: 60 + 300 + 250 + 210 + 90 = 910 [1]. 910 ÷ 50 = 18.2 minutes [1] [4] (b) Modal class: A is 20 < t ≤ 30, B is 10 < t ≤ 20 [1]. Clinic B had shorter waits on average (18.2 against 23.6 minutes) [1] [2] Examiner insight: Say the mean is an estimate because midpoints are assumed. Quote both modal classes.

7. (a) There are 9 values, so the median is the 5th. Without: 21 cm [1]. With: 25 cm [1] [2] (b) Without: 29 - 12 = 17 cm [1]. With: 33 - 18 = 15 cm [1] [2] (c) The median height was greater with fertiliser (25 cm against 21 cm), so fertiliser may help growth [1]. Caution: only 9 seedlings in each group, a small sample [1] [2] Examiner insight: Left-hand leaves are written outward from the stem, so read the key carefully. Attach a limit to any inference.

8. (a) Strong positive [1] [1] (b) Negative (strong or moderate) [1] [1] (c) No correlation [1] [1] Examiner insight: Give direction and strength together.

9. (a) Strong positive correlation [1] [1] (b) Correlation shows a link, not that one variable causes the other [1] [1] (c) Hot weather (or beach visitors) increases both sales [1] [1] Examiner insight: Link the extra factor to both quantities; a vague “other things” is weak.

10. (a) Strong negative correlation [1] [1] (b) Mean x = 48 ÷ 10 = 4.8 [1]. Mean y = 99.2 ÷ 10 = 9.92 [1] [2] (c) At x = 4.8 the line has y = 14.4 - 1.15(4.8 - 1) = 10.03, close to 9.92 [1] [1] (d) m = (5.2 - 14.4) ÷ (9 - 1) = -9.2 ÷ 8 = -1.15 [1]. 14.4 = -1.15(1) + c [1]. c = 15.55, so y = -1.15x + 15.55 [1] [3] (e) y = -1.15(6.5) + 15.55 = 8.075 hundred, about 810 drinks [1] [1] (f) About 115 fewer drinks are sold for each 1 °C rise in temperature [1] [1] (g) 20 °C is far outside the data (1 to 9). The line gives -7.45, an impossible number of drinks [1] [1] Examiner insight: For a gradient’s meaning, give units and direction (a fall). Check your equation against both given points.

11. (a) The pupil with 8 hours and 330 ms [1], because it is far above the downward trend (about 273 expected) [1] [2] (b) Mean x = 55 ÷ 8 = 6.875 [1]. Mean y = 2393 ÷ 8 = 299.1 (to 1 decimal place) [1] [2] (c) m = (250 - 342) ÷ (9 - 5) = -92 ÷ 4 = -23 [1]. 342 = -23(5) + c [1]. c = 457, so y = -23x + 457 [1] [3] (d) y = -23(7.2) + 457 = 291.4 ms [1] [1] (e) y = -23(10) + 457 = 227 ms [1]. Ten hours is outside the data range (5 to 9), so this extrapolation is unreliable [1] [2] Examiner insight: Identify the outlier by its values and leave it out when placing the line. Estimates inside the data range are safer.

Where marks are usually lost

• Using a pie chart angle as the frequency.
• Dividing by the new value in a percentage change.
• Quoting an average but no spread, or numbers for only one set.
• Not saying which direction is better (longer time is worse, longer battery life is better).
• Misreading the key on a back-to-back stem-and-leaf diagram.
• Writing “positive” or “weak” alone.
• Claiming correlation proves cause.
• Trusting an extrapolated estimate or missing an impossible value.

Next steps

• Revisit the revision notes and the study guide.
• Return to the course hub and tick off skills on the checklist.
• Try all free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

OxfordAQA International GCSE Mathematics (9260), specification Version 5.1 (for exams May/June 2018 onwards), published by OxfordAQA, section 3.4.2 Interpretation, references S6, S7 and S8.