CIE iGCSE Maths C9.5 Scatter diagrams Exam Style Practice Questions- Paper 3
Fidel gives different amounts of water to some plants.
The scatter diagram shows the height (cm) and the amount of water (ml) for each of 15 plants.
(a) Plot these two results on the scatter diagram.
(b) What type of correlation is shown in the scatter diagram?
(c) One of the plants had a lower height than expected for the amount of water given. On the scatter diagram, put a ring around the point for this plant.
(d) (i) On the scatter diagram, draw a line of best fit.
(ii) Another plant is given 65 ml of water. Use your line of best fit to estimate the height of this plant.
(e) Find the percentage of these 17 plants that have a height of more than 24 cm. Give your answer correct to 1 decimal place.
▶️ Answer/Explanation
(a) Ans: Two points accurately plotted
The points (40, 15) and (80, 35) are plotted on the scatter diagram.
(b) Ans: Positive
The scatter diagram shows an upward trend, indicating a positive correlation between water given and plant height.
(c) Ans: (60, 7) indicated
The point (60, 7) is circled as it lies significantly below the general trend.
(d)(i) Ans: Accurate straight line of best fit
A straight line is drawn passing through the middle of the data points, minimizing the distance from all points.
(d)(ii) Ans: 24 to 32
Using the line of best fit, for 65 ml of water, the estimated height is between 24 cm and 32 cm.
(e) Ans: 47.1
Out of 17 plants, 8 have heights > 24 cm. The percentage is calculated as $\left(\frac{8}{17}\right) \times 100 \approx 47.1\%$.
Visualizations:
(a) 
(b) 
(c) 
(d)(i) 
(d)(ii) 
(a) The scatter diagram shows the distance travelled and the cost for each of 12 taxi journeys.
(i) ‘The scatter diagram shows positive correlation.’ Is this statement true or false? Give a reason for your answer.
(ii) On one journey, the cost per kilometre travelled was much more expensive than on all of the other journeys. Draw a ring around this point on the scatter diagram.
(iii) Draw a line of best fit on the scatter diagram.
(iv) Another journey is 8 km long. Use your line of best fit to find an estimate for the cost of this journey.
(b) Arit, Luke and Marie share the cost of a taxi journey. The cost is \$26.40.
(i) Calculate how much Arit pays if they share the cost equally.
(ii) They decide to share the cost in proportion to the distance they each travel in the taxi. Arit travels 12 km, Luke travels 3 km and Marie travels 7.5 km.
- (a) Write the ratio 12 : 3 : 7.5 in its simplest form.
- (b) Calculate how much more Arit pays than if they share the cost equally.
(c) Jin invests some money from his taxi company.
He invests \$18,600 at a rate of 1.7% per year compound interest.
Calculate the value of the investment at the end of 6 years. Give your answer correct to the nearest dollar.
▶️ Answer/Explanation
(a)(i) True, because as the distance increases, the cost generally increases.
(a)(ii) The point at (1, 15) should be circled as it’s much higher than other points at similar distances.
(a)(iii) A straight line with positive gradient that follows the general trend of the points.
(a)(iv) About \$16-\$19 (from reading the line of best fit at 8 km).
(b)(i) \$26.40 ÷ 3 = \$8.80.
(b)(ii)(a) 12:3:7.5 simplifies to 8:2:5 (divided each by 1.5).
(b)(ii)(b) Total parts = 8+2+5 = 15. Arit pays (8/15)×\$26.40 = \$14.08. Difference from equal share = \$14.08 – \$8.80 = \$5.28.
(c) Using compound interest formula: \$18,600 × (1 + 0.017)^6 ≈ \$20,580 (rounded to nearest dollar).