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0580/32 May/Jun 2022, Question 5: Scatter Diagrams and Correlation

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 8 marks

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The question, in short

Rebecca records flight distance and ticket price for 12 journeys; complete the scatter diagram, describe correlation, identify highest price per km, draw a line of best fit, and estimate a ticket price using a scale drawing.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Plot the remaining four points from the table on the scatter diagram.

  1. 1Plot the last four points: (100, 120), (275, 170), (380, 310), (540, 305)

AnswerFour points correctly plotted

Part (b) · 1 mark

State the type of correlation shown by the scatter diagram.

  1. 1Longer flights tend to cost more: positive correlation

AnswerPositive

Part (c) · 1 mark

Ring the plotted point representing the journey with the greatest price per kilometre.

  1. 1Price per km: 220 ÷ 95 = 2.32, much higher than any other, e.g. 120 ÷ 100 = 1.2
  2. 2Ring the point (95, 220)

AnswerPoint at (95, 220) indicated

Part (d) · 1 mark

Draw a line of best fit on the scatter diagram.

  1. 1Draw a ruled line through the middle of the points following the upward trend, e.g. through the mean point (316, 230)

AnswerRuled line of best fit drawn

Part (e) · 3 marks

Use the scale drawing of K to L and your line of best fit to estimate the ticket price.

  1. 1Measure KL ≈ 6.4 cm
  2. 2Distance = 6.4 × 50 = 320 km
  3. 3Read up from 320 km to the line of best fit and across: ticket price ≈ $230

AnswerCorrect estimate supported by their line of best fit and a distance of 310 to 330 km

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