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A-LevelMathematicsProbability and statistics9709/51 · May/June 2024 · Q36 Marks

The heights, in cm, of 200 adults in Barimba are summarised in the following table. Height (h cm) 130 ≤ h < 150 150 ≤ h < 160 160 ≤ h < 170 170 ≤ h < 175 175 ≤ h < 195 Frequency 16 32 76 64 12

  1. (a)Draw a histogram to represent this information.[4]
  2. (b)The interquartile range is R cm. Show that R is not greater than 15.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [M1] At least four frequency densities calculated e.g. f/cw (16/20) or (32/10) or (76/10) or (64/5) or (12/20). Condone f/cw ±0.5 if unsimplified. Accept unsimplified, may be read from graph using their scale no lower than 1 cm = fd 2.
  2. [A1] All bar heights correct on graph, not FT. Using their suitable linear scale with at least three values indicated, no lower than 1 cm = fd 2.
  3. [B1] Bar ends at 150, 160, 170, 175, 195. Five bars drawn with a horizontal linear scale no lower than 1 cm = 10 cm, with at least three values indicated, 130 < horizontal scale < 195.
  4. [B1] Axes labelled frequency density (fd) height (h) and cm, OE, or an appropriate title. (Axes may be reversed)
  5. [M1] 170<h<175 – 160<h<170 UQ and LQ classes seen.
  6. [A1] 175 – 160 = 15 (If M0 scored, SC B1 for 175 – 160 = 15.)

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2024 Paper 5 Variant 1, question 3.

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