OxfordAQA International GCSE Mathematics: Statistical charts and diagrams (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.

The set below targets OxfordAQA International GCSE Mathematics (9260), using Version 5.1 of the specification (exams from May/June 2018), section 3.4.1, reference S4. Questions 10 to 12 are Extension only. The rest are Core content, which Extension papers can also assess. For drawing tasks, give the values you would plot.

If you get stuck, go to the study guide or the revision notes. For the wider course, see the checklist, the diagnostics and the course hub.

Questions

1. The number of passengers in 20 cars passing a school gate is: 1, 3, 2, 1, 1, 4, 2, 1, 3, 2, 1, 5, 2, 1, 2, 3, 1, 2, 4, 1. (a) Complete a tally chart and frequency table for 1 to 5 passengers. [3] (b) How many cars carried more than 2 passengers? [1]

2. A pictogram shows tickets sold for a school play. Key: one symbol = 12 tickets, and a half symbol = 6 tickets. Monday has 3 symbols, Tuesday has 2½ symbols and Wednesday has 4 symbols. On Thursday 54 tickets are sold. (a) How many tickets were sold on Tuesday? [1] (b) What should be drawn for Thursday? [2] (c) How many tickets were sold from Monday to Wednesday? [2]

3. A kiosk sells hot and cold drinks. A dual bar chart is drawn from this table.

Season	Spring	Summer	Autumn	Winter
Hot drinks	40	15	55	80
Cold drinks	25	90	30	10

(a) Give the two bar heights for autumn and say what the key must show. [2] (b) In which season is the difference between hot and cold sales greatest? Show your working. [2] (c) Show that more hot than cold drinks were sold over the year. [2]

4. A library records visitors on three days.

Day	Monday	Tuesday	Wednesday
Adults	18	14	20
Children	12	22	7

(a) A composite bar chart stacks children on top of adults. Give the height where each adult segment and each whole bar ends. [3] (b) Give one reason why the children’s numbers are harder to compare across days than the adults’. [1]

5. 90 pupils choose their favourite sport: football 33, swimming 24, tennis 15, cricket 18. (a) Calculate the sector angle for each sport on a pie chart. [3] (b) In a second survey of 150 pupils, the tennis sector is 84°. How many chose tennis? [2]

6. The water level of a reservoir (metres) at the start of each month is: January 12.4, February 13.1, March 14.8, April 15.6, May 14.2, June 11.9. It is shown on a line graph. (a) Between which two consecutive months was the increase greatest? [2] (b) Find the change in level from January to June. [2] (c) Estimate the level in mid-March and say why it is only an estimate. [2]

7. Journey times in minutes for 16 trips: 34, 18, 25, 41, 29, 33, 18, 47, 52, 26, 38, 29, 41, 22, 36, 29. (a) Show the times in an ordered stem-and-leaf diagram, including its key. [3] (b) Find the range. [1] (c) How many trips took more than 40 minutes, and which time occurs most often? [2]

8. An ice-cream stall records the midday temperature (°C) and the number of ice creams sold: (14, 22), (17, 31), (19, 38), (21, 41), (24, 55), (26, 58), (28, 70), (30, 64). These are plotted on a scatter graph. (a) State suitable scales for both axes. [2] (b) On a ninth day, (23, 15) lies well away from the other points. Suggest a reason that fits the context. [1] (c) Describe the pattern shown by the first eight points. [2]

9. The masses of 60 parcels are grouped as: 0 < m ≤ 2 (6 parcels), 2 < m ≤ 4 (14), 4 < m ≤ 6 (21), 6 < m ≤ 8 (13), 8 < m ≤ 10 (6). (a) Give the coordinates of the points for a frequency polygon. [3] (b) State the width and height of each bar of a histogram for these data. [2] (c) How many parcels have a mass greater than 6 kg? [1]

10. (Extension only) The daily time t minutes that 100 people spend on a phone: 0 < t ≤ 10 (8 people), 10 < t ≤ 30 (26), 30 < t ≤ 60 (45), 60 < t ≤ 120 (21). (a) Work out the frequency density for every class. [3] (b) Estimate how many people spent between 40 and 60 minutes. State your assumption. [2] (c) In another histogram a bar is 15 wide and 2.4 high. Find its frequency. [2] (d) Explain why the vertical axis is frequency density and not frequency. [1]

11. (Extension only) The times in seconds taken by 100 pupils to solve a puzzle: 0 < t ≤ 20 (3), 20 < t ≤ 40 (17), 40 < t ≤ 60 (25), 60 < t ≤ 80 (25), 80 < t ≤ 100 (20), 100 < t ≤ 120 (10). (a) Write the cumulative frequencies. [2] (b) Say how the points of a cumulative frequency diagram are plotted. [2] (c) From the diagram, estimate the median and the spread of the middle half of the times (the interquartile range). [4] (d) Estimate how many pupils took more than 90 seconds. [2]

12. (Extension only) Test marks for two classes. Class X: minimum 12, lower quartile 25, median 34, upper quartile 41, maximum 55. Class Y: minimum 18, lower quartile 30, median 33, upper quartile 36, maximum 49. (a) Find the interquartile range and the range for Class X. [2] (b) Describe the box plot for Class Y on a scale from 10 to 60. [2] (c) Compare the two classes. [3]

Answers

1. (a) Counting gives 1 → 8, 2 → 6, 3 → 3, 4 → 2, 5 → 1 [1]. Tally marks match: ||||/ |||, ||||/ |, |||, ||, | [1]. Frequencies total 20 [1]. [3] (b) 3 + 2 + 1 = 6 [1]. 6 cars [1] Examiner insight: Total the frequencies and compare with the values given.

2. (a) 2.5 × 12 = 30 [1]. 30 tickets [1] (b) 54 ÷ 12 = 4.5 [1]. 4 whole symbols and 1 half symbol [1]. [2] (c) Monday 3 × 12 = 36 and Wednesday 4 × 12 = 48 [1]. 36 + 30 + 48 = 114 [1]. [2] Examiner insight: Divide or multiply by the key first. Writing the 4.5 shows your method even if the drawing slips.

3. (a) Autumn: hot 55, cold 30 [1]. The key must show which colour means hot and which cold [1]. [2] (b) Differences: spring 15, summer 75, autumn 25, winter 70 [1]. Summer, by 75 [1]. [2] (c) Hot: 40 + 15 + 55 + 80 = 190 [1]. Cold: 25 + 90 + 30 + 10 = 155, and 190 > 155, so more hot drinks [1]. [2] Examiner insight: For “show that”, write both totals and the comparison.

4. (a) Adult segments end at 18, 14 and 20 [1]. Adding children gives 30 for Monday and 36 for Tuesday [1]. Wednesday ends at 27 [1]. [3] (b) The children’s segments do not start at the same baseline [1]. [1] Examiner insight: Stacked heights are running totals, so add the segments.

5. (a) 360° ÷ 90 = 4° per pupil [1]. Football 33 × 4 = 132°, swimming 24 × 4 = 96° [1]. Tennis 15 × 4 = 60°, cricket 18 × 4 = 72°, and 132 + 96 + 60 + 72 = 360° [1]. [3] (b) (84 ÷ 360) × 150 [1] = 35 pupils [1]. [2] Examiner insight: Check the angles total 360° before you draw.

6. (a) Increases: 0.7, 1.7, 0.8 (and May and June fall) [1]. February to March, by 1.7 m [1]. [2] (b) 11.9 − 12.4 [1] = −0.5 m, a fall of 0.5 m [1]. [2] (c) (14.8 + 15.6) ÷ 2 = 15.2 m [1]. It is an estimate because the level was not measured mid-month [1]. [2] Examiner insight: Give the pair of months and the size of the change.

7. (a) Stems 1 to 5 [1]. Ordered leaves: 1 | 8 8; 2 | 2 5 6 9 9 9; 3 | 3 4 6 8; 4 | 1 1 7; 5 | 2 [1]. Key: 2 | 5 means 25 minutes [1]. [3] (b) 52 − 18 = 34 minutes [1]. [1] (c) Over 40: 41, 41, 47, 52, so 4 trips [1]. The most common time is 29 minutes [1]. [2] Examiner insight: Order the leaves and include the key.

8. (a) Horizontal: 12 to 32 °C in steps of 2 [1]. Vertical: 0 to 80 in steps of 10 [1]. [2] (b) For example, rain or an early closure, so few were sold despite the temperature [1]. [1] (c) As temperature rises, sales generally rise [1]. The points lie in a rising band, with a small dip at 30 °C [1]. [2] Examiner insight: Use context: “hotter days sell more” says more than “the points go up”.

9. (a) Midpoints 1, 3, 5, 7, 9 [1]. Points (1, 6), (3, 14), (5, 21), (7, 13), (9, 6) [1]. Joined with straight lines [1]. [3] (b) Each bar is 2 wide (touching) [1]. Heights 6, 14, 21, 13, 6, because the classes are equal [1]. [2] (c) 13 + 6 = 19 parcels [1]. [1] Examiner insight: Write the midpoints first.

10. (a) Frequency density = frequency ÷ width [1]. Densities 0.8, 1.3 [1], 1.5, 0.35 [1]. [3] (b) 20 × 1.5 [1] = 30 people, assuming people are spread evenly across 30 to 60 [1]. [2] (c) 2.4 × 15 [1] = 36 [1]. [2] (d) Class widths differ, so heights alone would mislead; area shows frequency [1]. [1] Examiner insight: Write out each division by class width, so a single error does not hide the rest of your method.

11. (a) 3, 20, 45, 70, 90, 100 [2]. [2] (b) Plot each cumulative frequency against the upper class boundary, such as (20, 3) and (40, 20) [1], start at (0, 0) and join with a smooth curve [1]. [2] (c) Median is at n ÷ 2 = 50th value [1], reading about 64 seconds [1]. Lower quartile at the 25th value is about 44, upper quartile at the 75th is about 85 [1]. Interquartile range about 85 − 44 = 41 seconds [1]. [4] (d) At 90 seconds the cumulative frequency is about 80 [1]. 100 − 80 = 20 pupils [1]. [2] Examiner insight: Draw reading lines on the curve, so a slightly different reading still shows your method.

12. (a) Interquartile range 41 − 25 = 16 [1]. Range 55 − 12 = 43 [1]. [2] (b) Mark 18, 30, 33, 36 and 49 on the scale [1]. Draw a box from 30 to 36 with a line at 33, and whiskers to 18 and 49 [1]. [2] (c) Medians are close: 34 for X, 33 for Y [1]. Interquartile ranges: 16 for X, 6 for Y [1]. So Y is more consistent and X more varied [1]. [3] Examiner insight: A comparison is stronger with one statement about an average and one about spread, each with figures.

Where marks are usually lost

• Leaving out the key on a pictogram, dual bar chart or stem-and-leaf diagram.
• Plotting a polygon at class edges, not midpoints.
• Sector angles that fail to total 360°.
• Using frequency as a bar height for unequal classes. Work out each frequency density.
• Plotting cumulative frequency at the lower boundary, or reading the median at the wrong position.
• Comparing box plots with no figures, or using only the median.
• Quoting curve readings as exact. Say “about”.

Next steps

• Recap formulas and methods in the revision notes.
• Return to the study guide for any chart you found hard.
• Use the checklist to record progress, and the hub for other units.
• Check your level with a free 10-minute diagnostic.
• Want a tutor’s help? Book a free trial class.

Official syllabus

Specification used: Version 5.1 of the OxfordAQA specification for International GCSE Mathematics (9260), which is for exams May/June 2018 onwards. Section 3.4.1, Presentation and analysis, reference S4.