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A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2019 · Q58 Marks

Ransha measured the lengths, in centimetres, of 160 palm leaves. His results are illustrated in the cumulative frequency graph below. [Figure with cumulative frequency graph]

  1. (i)Estimate how many leaves have a length between 14 and 24 centimetres.[1]
  2. (ii)10% of the leaves have a length of L centimetres or more. Estimate the value of L.[2]
  3. (iii)Estimate the median and the interquartile range of the lengths.[3]
  4. (iv)Sharim measured the lengths, in centimetres, of 160 palm leaves of a different type. He drew a box-and-whisker plot for the data, as shown on the grid below. Compare the central tendency and the spread of the two sets of data.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [B1] 98 ≤ answer < 100
  2. [M1] 144 seen, may be marked on graph
  3. [A1] (L =) 22
  4. [B1] 15.5 < median < 15.8
  5. [M1] 18.5 < UQ < 19 – 12.5 < LQ < 13
  6. [A1] 6.0 ≤ IQR < 6.2
  7. [B1] Any correct comparison of central tendency, must mention median
  8. [B1] Any correct comparison of spread, must refer to IQR

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 6 Variant 1, question 5.

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