Cambridge IGCSE Statistics: Scatter diagrams, correlation, lines of best fit and estimation (0479) – 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 Topic 11, Bivariate distributions, of the Cambridge IGCSE Statistics 0479 syllabus for examination in 2027 (outcomes 11.1 to 11.7). You will need a ruler and graph paper for questions 4 and 9. Use the study guide or the revision notes first. The Cambridge IGCSE Statistics hub and the printable checklist show the full course.

Questions

1. For each pair, state which variable is the independent variable.

(a) The speed of a car and its stopping distance. [1] (b) The number of adverts shown and the number of sales made. [1] (c) The number of days since a seed was planted and the height of the plant. [1]

2. The table shows the distance from a city centre and the monthly rent for six flats.

Distance (km)	2	4	6	8	10	12
Rent (£)	1380	1250	1090	960	790	680

(a) State the type of correlation. [1] (b) Describe what this means for the flats. [1] (c) State which variable is independent. [1]

3. State the type of correlation you would expect for each.

(a) The maximum daily temperature and the number of ice lollies sold at a kiosk. [1] (b) The length of a person’s surname and their height. [1] (c) The age of a car and its value. [1] (d) Points forming a narrow band that rises from bottom left to top right. [1]

4. A gardener gives eight identical plants different amounts of water each day (x ml) and measures the growth in a week (y mm).

x (ml)	10	20	30	40	50	60	70	80
y (mm)	12	18	21	27	10	34	38	43

(a) Plot a scatter diagram on graph paper. [3] (b) Describe the correlation. [1] (c) Identify the point that does not fit the pattern. [1]

5. A courier records the distance (x km) and the delivery charge (y pounds) for several deliveries between 20 km and 80 km. A line of best fit passes through (20, 31) and (80, 73).

(a) Find the gradient of the line. [2] (b) Find the equation of the line in the form y = mx + c. [2] (c) Estimate the charge for a delivery of 50 km. [1] (d) Estimate the distance for a charge of 45 pounds. [2]

6. A kiosk records the hours of sunshine (x) and the ice lollies sold (y) on six days, in this order.

x	8	2	12	6	4	10
y	31	15	45	24	21	38

(a) Use the method of semi-averages to find the two points through which the line of best fit passes. [3] (b) Find the equation of the line. [3] (c) Estimate the sales on a day with 7 hours of sunshine. [1]

7. A café uses the line y = 4x − 12 to estimate the cups of iced tea sold (y) from the midday temperature in °C (x). The line was fitted to data with x between 10 and 28.

(a) Estimate the sales when x = 20. [1] (b) Estimate the sales when x = 35, and say whether this estimate is more or less reliable than the one in part (a). [2] (c) Find the value of y when x = 2 and comment. [2] (d) State one assumption made when using the line. [1]

8. The line of best fit y = 12x + 150 estimates the cost in pounds (y) of a party from the number of guests (x). The data covered 20 to 100 guests.

(a) Explain what the gradient 12 means here. [2] (b) Explain what the value 150 means here, and comment on it. [2]

9. A park manager records the midday temperature (x °C) and the number of visitors (y) on ten days.

x	10	3	15	7	2	13	8	16	5	11
y	64	48	74	56	46	70	57	76	53	66

(a) Plot a scatter diagram. [3] (b) Describe the correlation. [1] (c) Use semi-averages to find the two points on the line of best fit. [3] (d) Find the equation of the line in the form y = mx + c. [3] (e) Estimate the visitors when x = 12. [1] (f) Explain why an estimate for x = 30 would be unreliable. [1]

10. Describe the correlation in each table, where x = 1, 2, 3, … 8 in order.

Table	y values
P	5, 7, 9, 12, 14, 16, 19, 21
R	16, 12, 17, 9, 15, 10, 13, 11
S	10, 4, 12, 5, 11, 3, 12, 6

(a) Table P. [1] (b) Table R. [1] (c) Table S. [1] (d) State which table would give the most reliable estimates from a line of best fit, with a reason. [1]

11. A restaurant records the number of staff on duty (x) and the customers served per hour (y). The pairs were written down in this order: (6, 22), (2, 11), (9, 30), (4, 18), (1, 8), (8, 28), (3, 15), (7, 24). Sam splits them into the first four and the last four, and finds the mean point of each.

(a) Explain Sam’s mistake. [1] (b) Find the two correct semi-average points. [2] (c) Find the equation of the line of best fit. [3] (d) Estimate y when x = 10. [1]

Answers

1. (a) Speed. [1] (b) The number of adverts. [1] (c) The number of days. [1] [3] Examiner insight: Name the variable, not just “the first one”. Say which value you would use to predict the other and the answer is usually clear.

2. (a) Strong negative correlation. [1] (b) Flats further from the centre tend to have lower rent. [1] (c) Distance from the city centre. [1] [3] Examiner insight: A description needs both direction and strength, and a context statement shows you know what the correlation means. “Negative” on its own is incomplete.

3. (a) Positive. [1] (b) No correlation. [1] (c) Negative. [1] (d) Strong positive. [1] [4] Examiner insight: “None” is a different answer from “weak”. If there is no reason for the variables to be related, say no correlation.

4. (a) Axes labelled with units and scales that use the grid. [1] At least six points plotted accurately. [1] All eight points plotted accurately. [1] (b) Positive correlation (strong apart from one point). [1] (c) The point (50, 10). [1] [5] Examiner insight: Plot with small, exact crosses and check each one against the table. Reading a scale wrongly by one square is an easy way to lose credit on a plot.

5. (a) Gradient = (73 − 31)/(80 − 20). [1] = 42/60 = 0.7. [1] (b) 31 = 0.7 × 20 + c, so c = 31 − 14 = 17. [1] y = 0.7x + 17. [1] (c) y = 0.7 × 50 + 17 = 52 pounds. [1] (d) 45 = 0.7x + 17, so 0.7x = 28. [1] x = 40 km. [1] [7] Examiner insight: Show the subtraction and the substitution. Clear working for each part makes your method visible even if an earlier value is wrong.

6. (a) Sorted by x: (2, 15), (4, 21), (6, 24) | (8, 31), (10, 38), (12, 45). [1] Lower mean = (4, 20). [1] Upper mean = (10, 38). [1] (b) Gradient = (38 − 20)/(10 − 4) = 18/6 = 3. [1] 20 = 3 × 4 + c, so c = 8. [1] y = 3x + 8. [1] (c) y = 3 × 7 + 8 = 29 ice lollies. [1] [7] Examiner insight: Write the sorted list before taking means. It shows the split is correct, and the question gives the data out of order on purpose.

7. (a) y = 4 × 20 − 12 = 68 cups. [1] (b) y = 4 × 35 − 12 = 128 cups. [1] Less reliable, because 35 is outside the range of the data (10 to 28), so it is extrapolation. [1] (c) y = 4 × 2 − 12 = −4. [1] Sales cannot be negative, so the line does not work outside its range. [1] (d) Any one: the straight-line pattern continues; the sample represents all days; other factors such as weather are unchanged. [1] [6] Examiner insight: “It is further away” is a weaker reason than “outside the range of the data”. Link the reason to the range given in the question.

8. (a) Each extra guest adds about 12 pounds to the cost. [1] The cost is estimated to rise by 12 pounds per guest. [1] (b) 150 pounds is the estimated cost with no guests, a fixed cost. [1] No guests is outside the data (20 to 100 guests), so this value should be treated with care. [1] [4] Examiner insight: Give a rate with units for the gradient, and say what the intercept means in the real situation. Answers that say only “the y-intercept” give the marker nothing to credit.

9. (a) Axes labelled with suitable scales. [1] At least eight points correct. [1] All ten points correct. [1] (b) Strong positive correlation. [1] (c) Sorted by x: (2, 46), (3, 48), (5, 53), (7, 56), (8, 57) | (10, 64), (11, 66), (13, 70), (15, 74), (16, 76). [1] Lower mean: x = 25/5 = 5, y = 260/5 = 52, so (5, 52). [1] Upper mean: x = 65/5 = 13, y = 350/5 = 70, so (13, 70). [1] (d) Gradient = (70 − 52)/(13 − 5) = 18/8 = 2.25. [1] 52 = 2.25 × 5 + c, so c = 52 − 11.25 = 40.75. [1] y = 2.25x + 40.75. [1] (e) y = 2.25 × 12 + 40.75 = 67.75, so about 68 visitors. [1] (f) 30 °C is far outside the data (2 to 16 °C), so this is extrapolation and the pattern may not continue. [1] [12] Examiner insight: In a long question, label each part and show the sorted list and both mean points. A slip in part (c) is easier to follow when the working is laid out.

10. (a) Strong positive correlation. [1] (b) Weak negative correlation. [1] (c) No correlation. [1] (d) Table P, because its points lie close to a straight line. [1] [4] Examiner insight: For tables, look at the general direction of y as x increases, then at how steady it is. Table R falls overall but jumps about, so it is weak rather than strong.

11. (a) The pairs must first be sorted by x, so the groups should be the four smallest and four largest x-values. [1] (b) Lower group (1, 8), (2, 11), (3, 15), (4, 18): mean = (2.5, 13). [1] Upper group (6, 22), (7, 24), (8, 28), (9, 30): mean = (7.5, 26). [1] (c) Gradient = (26 − 13)/(7.5 − 2.5) = 13/5 = 2.6. [1] 13 = 2.6 × 2.5 + c, so c = 6.5. [1] y = 2.6x + 6.5. [1] (d) y = 2.6 × 10 + 6.5 = 32.5 customers per hour. [1] [7] Examiner insight: The explanation in part (a) needs to say that the data must be ordered by the x-values, not just that Sam’s groups are wrong.

Where marks are usually lost

• Giving only “positive” or “negative” without strength, or without context.
• Plotting points inaccurately, or using a scale that wastes the grid.
• Joining points with a zigzag instead of drawing one ruled straight line.
• Not sorting by x before splitting the data into halves.
• Subtracting in different orders in the gradient and getting the wrong sign.
• Giving an extrapolated estimate with no comment, or not noticing when it is impossible.
• Giving a gradient meaning with no units or no context.

Next steps

• Review the unit in the revision notes and the study guide.
• See the Cambridge IGCSE Statistics hub and the printable checklist.
• Take the free 10-minute diagnostics to find your weakest topics.
• Book a free trial class if you would like help from a teacher.

Official syllabus

Cambridge IGCSE Statistics 0479 syllabus for examination in 2027, Topic 11 Bivariate distributions, published by Cambridge University Press & Assessment (Cambridge International).