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0580/32 May/Jun 2023, Question 4: Expressing One Quantity as a Percentage

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

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The question, in short

Using a scatter graph of plant height against water volume for 15 plants, add two more data pairs, describe the correlation, identify an outlier, fit a line, estimate a height, and find a percentage.

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

Part (a) · 1 mark

Add the two given water-and-height pairs to the scatter diagram.

  1. 1Plot (60, 27) and (85, 41) with crosses like the other points

AnswerTwo points accurately plotted

Part (b) · 1 mark

State the kind of correlation the scatter diagram displays.

  1. 1As the amount of water increases, the height increases
  2. 2Positive correlation

AnswerPositive

Part (c) · 1 mark

Ring the plotted point where the plant grew less tall than its water amount would suggest.

  1. 1(60, 7) is far below the trend of the other points
  2. 2Ring the point (60, 7)

Answer(60, 7) indicated

Part (di) · 1 mark

Draw a straight line that best fits the plotted points.

  1. 1Mean point: water = 915 ÷ 17 ≈ 54, height = 412 ÷ 17 ≈ 24
  2. 2Draw a ruled line through about (54, 24) following the trend, e.g. from about (0, 6) to (100, 40)

AnswerAccurate straight line of best fit

Part (dii) · 1 mark

Using your fitted line, estimate the height for a plant given 65 ml of water.

  1. 1Go up from 65 ml to the line of best fit and across to the height axis
  2. 2Height ≈ 28 cm

Answer24 to 32

Part (e) · 3 marks

Including the two added pairs, work out the percentage of the 17 plants taller than 24 cm, to 1 decimal place.

  1. 1Heights over 24 cm: 26, 29, 25, 36, 39, 47, 27, 41 = 8 plants
  2. 28/17 × 100 = 47.05…
  3. 3≈ 47.1%

Answer47.1

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