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4024/21 May/Jun 2024, Question 2: Estimating the Mean for Grouped Data

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Using a table of midday temperatures at ten mountain heights, complete and interpret a scatter diagram, then estimate a mean time and a histogram bar height from grouped data for 80 adults.

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

Part (ai) · 2 marks

Plot the remaining five height and temperature pairs from the table onto the given scatter diagram.

  1. 1Plot (100, 3.5), (1250, −4.6), (1450, −6.4), (1125, −4.0) and (1350, −3.8)

AnswerComplete scatter diagram

Part (aii) · 1 mark

State what kind of correlation the plotted points show.

  1. 1As height increases, temperature decreases: negative correlation

AnswerNegative

Part (aiii) · 1 mark

Add a line of best fit to the scatter diagram.

  1. 1Rule a straight line through the middle of the points, sloping down, with about as many points above as below
  2. 2It should pass near the mean point (832.5, −1.38)

AnswerRuled line of best fit

Part (aiv) · 1 mark

Using your line of best fit, estimate the temperature at a height of 1000 m.

  1. 1Go up from 1000 m to your line, then across to the temperature axis
  2. 2A good line gives about −2.5 °C (your value depends on your line)

Answer−2.6 (accept −3.1 to −2.1)

Part (bi) · 3 marks

From the grouped frequency table of 80 adults' climb times, work out an estimated mean time.

  1. 1Midpoints: 6, 7, 7.75, 8.25, 9.5
  2. 2Σfx = 6×8 + 7×15 + 7.75×20 + 8.25×23 + 9.5×14 = 48 + 105 + 155 + 189.75 + 133 = 630.75
  3. 3Mean = 630.75 ÷ 80 = 7.884… ≈ 7.88 hours

Answer7.88 or 7.884…

Part (bii) · 1 mark

Given the 5.5 < h ≤ 6.5 bar is 8 mm tall, find the height of the bar for 8 < h ≤ 8.5.

  1. 15.5 < h ≤ 6.5: frequency density = 8 ÷ 1 = 8, shown by 8 mm, so 1 mm per unit
  2. 28 < h ≤ 8.5: frequency density = 23 ÷ 0.5 = 46
  3. 3Height = 46 mm

Answer46

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Also searched as: 4024/21/M/J/24 · 4024_s24_qp_21 · 4024 s24 21 · question 2.
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