Cambridge O Level Mathematics: Scatter Diagrams, Correlation and Cumulative Frequency Diagrams (4024) – 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 cover sections 9.5 (Scatter diagrams) and 9.6 (Cumulative frequency diagrams) of the Cambridge O Level Mathematics (Syllabus D) 4024 syllabus for 2025, 2026 and 2027. The syllabus is not tiered. You need graph paper and a ruler. Readings from hand-drawn curves differ slightly, so answers near the stated values are reasonable. Use the study guide first if you need the methods, or the revision notes for a quick recap. The course hub and printable checklist cover the rest of the syllabus.

Questions

1. State whether you expect positive, negative or zero correlation between each pair of quantities. (a) The hours of daylight in a day and the amount of electricity used for lighting. [1] (b) The age of a child, from 5 to 12 years, and the child’s height. [1] (c) The telephone numbers of pupils in a class and their test marks. [1]

2. Eight students recorded their daily screen time, x hours, and the hours of sleep they had that night, y hours.

x	1	2	2.5	3	4	4.5	5	6.5
y	9.1	8.8	8.2	8.0	7.4	7.5	6.6	6.0

(a) Plot the eight points on a scatter diagram, with x from 0 to 7 and y from 5 to 10. [2] (b) Describe the correlation. [1] (c) Draw a line of best fit and use it to estimate the sleep for a student with 5.5 hours of screen time. [3]

3. Three pupils each draw a “line of best fit” on the same scatter diagram. Pupil A draws a line that stops halfway along the data. Pupil B draws a smooth curve through the points. Pupil C draws a ruled line with every point above it. Explain what is wrong with each. [3]

4. A shop records the price, x pence, of a notebook and the number sold per day, y. A line of best fit is drawn through (20, 70) and (60, 40). (a) Calculate the gradient of the line. [2] (b) Explain what the gradient means in this context. [1] (c) Find the equation of the line in the form y = mx + c. [2] (d) Use the line to estimate the number sold when the price is 50 pence. [1] (e) Explain why the line should not be used for a price of 120 pence. [1]

5. The masses of 100 parcels, m kg, are summarised below.

Mass	0 < m ≤ 10	10 < m ≤ 20	20 < m ≤ 30	30 < m ≤ 40	40 < m ≤ 50	50 < m ≤ 60
Frequency	7	19	31	24	14	5

Complete a cumulative frequency table for these data and show how you can check it. [3]

6. Use your table from question 5. Write down the coordinates of the points you would plot for a cumulative frequency diagram, and describe how you mark and join them. [3]

7. Draw the cumulative frequency diagram for question 5 and use it to estimate the median, the lower quartile, the upper quartile and the interquartile range. [4]

8. Use your diagram from question 7. (a) Estimate the number of parcels heavier than 45 kg. [2] (b) Write your answer to part (a) as a percentage of all the parcels. [1] (c) The heaviest 10% of parcels need special handling. Estimate the mass above which a parcel needs special handling. [2]

9. The ages of 100 members of a club are summarised by this cumulative frequency table.

Age, x years	x ≤ 20	x ≤ 40	x ≤ 60	x ≤ 80	x ≤ 100
Cumulative frequency	12	35	a	88	100

The frequency for 40 < x ≤ 60 is 31. (a) Find a. [1] (b) Find the frequencies for 60 < x ≤ 80 and 80 < x ≤ 100. [2] (c) State the class that contains the median. [1]

10. The ages of 100 customers at each of two cafés were recorded.

Age, x years	x ≤ 20	x ≤ 30	x ≤ 40	x ≤ 50	x ≤ 60	x ≤ 70
Café A	0	6	23	58	84	100
Café B	0	11	40	78	93	100

(a) Draw both cumulative frequency curves on one grid and estimate the median and interquartile range for Café A. [2] (b) Estimate the median and interquartile range for Café B. [2] (c) Compare the ages of customers at the two cafés. [2]

11. A student draws a cumulative frequency diagram for 80 values. She plots each point at the middle of its class, does not plot a starting point, joins the points with a ruler, and reads the lower quartile at height 25. (a) Identify three errors. [3] (b) State the three heights she should use for the lower quartile, the median and the upper quartile. [2]

Answers

1. (a) More daylight means less lighting is needed, so negative correlation. [1] (b) Children grow as they get older, so positive correlation. [1] (c) There is no link between a telephone number and a mark, so zero correlation. [1] Examiner insight: Name the type and give a reason tied to the context. A bare word is a weaker answer than a short explanation.

2. (a) The eight points are plotted correctly, for example (1, 9.1) and (6.5, 6.0). [1] Each is marked clearly, as a small cross. [1] (b) The points fall from left to right: strong negative correlation. More screen time goes with less sleep. [1] (c) Mean x = 28.5 ÷ 8 ≈ 3.56 and mean y = 61.6 ÷ 8 = 7.7, so a line through about (3.56, 7.7) is a good guide. [1] Rule one straight line across all the data with points balanced on both sides. [1] Reading at x = 5.5 gives about 6.6 hours (anything from 6.4 to 6.8 is reasonable). [1] Examiner insight: Show guide lines on your graph, so an estimate has visible working.

3. Pupil A: the line does not extend across the full data set. [1] Pupil B: a line of best fit should be a single ruled straight line, not a curve. [1] Pupil C: there should be a roughly even distribution of points either side of the line, but all the points are on one side. [1] Examiner insight: Match each fault to a property of a good line. One reason per pupil is enough.

4. (a) Gradient = (40 − 70) ÷ (60 − 20). [1] = −30 ÷ 40 = −0.75. [1] (b) For each extra 1 pence in price, about 0.75 fewer notebooks are sold per day (3 fewer for every 4 pence). [1] (c) y = −0.75x + c. Using (20, 70): 70 = −15 + c. [1] c = 85, so y = 85 − 0.75x. [1] (d) y = 85 − 0.75 × 50 = 47.5, so about 47 or 48 notebooks. [1] (e) At 120 pence the equation gives 85 − 90 = −5, which is impossible. The price is far outside the data, so the straight-line pattern may not continue. [1] Examiner insight: In part (b) mention both variables, such as “per 1 pence” and “notebooks sold”.

5. Cumulative frequencies: 7, 7 + 19 = 26, 26 + 31 = 57, 57 + 24 = 81, 81 + 14 = 95, 95 + 5 = 100. [2]

Mass	m ≤ 10	m ≤ 20	m ≤ 30	m ≤ 40	m ≤ 50	m ≤ 60
Cumulative frequency	7	26	57	81	95	100

Check: the last value, 100, equals the total number of parcels. [1] Examiner insight: Show each running total so that one slip is easy to find.

6. Points: (0, 0), (10, 7), (20, 26), (30, 57), (40, 81), (50, 95), (60, 100). [1] Each cumulative frequency goes at its upper class boundary, and (0, 0) is the start point where the first class begins. [1] Mark each point with a small cross and join them with a smooth curve, not with ruled lines. [1] Examiner insight: Crosses at the upper boundary, a start point and a smooth curve are three separate things to check on your own diagram.

7. The heights to read are 25, 50 and 75. [1] Median: about 28 kg. [1] Lower quartile about 19.5 kg and upper quartile about 37.5 kg. [1] IQR = 37.5 − 19.5 = about 18 kg. [1] Examiner insight: Write each reading down. An IQR is a difference, so give one number with a unit.

8. (a) Up from 45 kg to the curve, then across: about 88 parcels weigh 45 kg or less. [1] So 100 − 88 = 12 parcels weigh more than 45 kg. [1] (b) 12 ÷ 100 × 100 = 12%. [1] (c) The heaviest 10% lie above the 90th percentile, at height 0.9 × 100 = 90. [1] Reading across at 90 gives about 46 kg. [1] Examiner insight: The curve counts values at or below a point. “Heavier than” needs a subtraction from the total, and “the heaviest 10%” points to the 90th percentile.

9. (a) a is the cumulative frequency at x ≤ 60: 35 + 31 = 66. [1] (b) For 60 < x ≤ 80: 88 − 66 = 22. [1] For 80 < x ≤ 100: 100 − 88 = 12. [1] (c) The median is the 50th value. Since 35 < 50 ≤ 66, it lies in the class 40 < x ≤ 60. [1] Examiner insight: The median class is a class, not a number. Quote the whole class interval, such as 40 < x ≤ 60.

10. (a) Heights 25, 50 and 75 on Café A’s curve give a lower quartile of about 40.6, a median of about 48 years and an upper quartile of about 56.5. [1] IQR = 56.5 − 40.6 = about 16 years. [1] (b) For Café B the lower quartile is about 34.8, the median about 43 years and the upper quartile about 49.2. [1] IQR = 49.2 − 34.8 = about 14 years. [1] (c) Café A’s median is higher (about 48 against 43), so its customers are typically older. [1] Café B’s IQR is smaller (about 14 against 16), so its customers’ ages are more consistent. [1] Examiner insight: Compare an average and a spread, and say what each means for the customers. Quoting the numbers alone is not a comparison.

11. (a) Any three of: plotting at class midpoints instead of upper boundaries; no starting point at the lower boundary of the first class; joining with a ruler instead of a smooth curve; reading the lower quartile at height 25 instead of the correct height. [3] (b) For n = 80: lower quartile at 80 ÷ 4 = 20, median at 80 ÷ 2 = 40, upper quartile at 3 × 80 ÷ 4 = 60. [2] Examiner insight: Quartile heights depend on n, so always work out n ÷ 4 before you read the graph. Never assume 25.

Where marks are usually lost

• Plotting at class midpoints instead of upper class boundaries.
• Forgetting the starting point (lower boundary of the first class, 0).
• Joining a cumulative frequency graph with ruled segments, or drawing a line of best fit as a curve.
• Using the wrong height for quartiles and percentiles, for example 25 whatever the total.
• Reading a count at or below a value when the question asks for “more than”, without subtracting from n.
• Describing correlation without naming its type, or without a reason from the context.
• Using a line of best fit far outside the data and giving no warning.

Next steps

• Revise with the revision notes and the study guide.
• Return to the O Level Mathematics hub and tick off the printable checklist.
• Take the free 10-minute diagnostics to find your weakest topics.
• Book a free trial class if you want help with any of this.

Official syllabus

Cambridge O Level Mathematics (Syllabus D) 4024 syllabus for 2025, 2026 and 2027, published by Cambridge University Press & Assessment (Cambridge Assessment International Education), sections 9.5 and 9.6.