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4024/21 Oct/Nov 2022, Question 2: Estimating the Mean for Grouped Data

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Using a table of ages and heights for 10 boys, plot missing points, add a best-fit line, estimate a height at age 14, and judge whether the line suits age 22; then use a grouped frequency table of 180 girls' heights to find a percentage and estimate the mean.

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

Part (ai) · 2 marks

Plot the four remaining age-height pairs from the table onto the given scatter diagram.

  1. 1Plot the remaining points: (13, 158), (17, 175), (13, 150), (16, 160)

AnswerFour points plotted correctly

Part (aii) · 1 mark

Add a straight line of best fit to the completed scatter diagram.

  1. 1Rule a straight line through the middle of the points, following the upward trend
  2. 2It should pass close to the mean point (13.5, 155.1), with about as many points above it as below

AnswerRuled line of best fit

Part (aiii) · 1 mark

From your line, read off the predicted height for a boy aged 14 years.

  1. 1Go up from 14 on the Age axis to the line, then across to the Height axis
  2. 2For a line through (13.5, 155.1) with gradient about 4.4: 155.1 + 0.5 × 4.4 ≈ 157 cm

Answer157 (accept 152 to 162)

Part (aiv) · 1 mark

Give a reason why extrapolating your line to age 22 is unreliable.

  1. 1The data only covers ages 10 to 18
  2. 222 is outside the range of the data, so the line cannot be relied on (extrapolation)

AnswerAge outside range of given data

Part (bi) · 2 marks

Find what percentage of the 180 girls have heights above 145 cm.

  1. 1Taller than 145 cm: 62 + 24 = 86 girls
  2. 286/180 × 100 = 47.77… ≈ 47.8%

Answer47.8 or 47.77 to 47.78

Part (bii) · 3 marks

Using midpoints of the height classes, work out an estimated mean height.

  1. 1Midpoints: 130, 137.5, 142.5, 147.5, 155
  2. 2Σfx = 130×8 + 137.5×31 + 142.5×55 + 147.5×62 + 155×24
  3. 3= 1040 + 4262.5 + 7837.5 + 9145 + 3720 = 26 005
  4. 4Mean = 26 005 ÷ 180 = 144.47… ≈ 144 cm

Answer144 or 144.4 to 144.5

Stuck on a step? Read the free lesson: Estimating the Mean for Grouped Data

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Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 2.
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