UniGeniusGCSE Maths · Edexcel 1MA1

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Box plots and distribution comparisons

3 exam-style questions. Answers and the mark for each step are on the last page.

  1. Question 1Non-calculator · 2 marks

    Here are the times, in minutes, of 11 runners, in order: 3, 5, 6, 8, 9, 11, 12, 14, 15, 18, 21.

    (a) Work out the interquartile range. (2)

  2. Question 2Non-calculator · 5 marks

    The ordered data are 2, 4, 7, 9, 12, 14, 16, 20. Take Q1 as the median of the lower four values and Q3 as the median of the upper four values.

    (a) Find the interquartile range. (3)

    (b) Find the median. (2)

  3. Question 3Non-calculator · 4 marks

    (a) Nine non-negative whole numbers are written in ascending order. Their mean is 18, their median is 22 and their range is 30. The largest number is 36. Work out the greatest possible value of the seventh number. Show that your value is possible. (4)

Answers and marks

Question 1

(a) 9 minutes

  • M1 Both quartiles, 6 and 15.
  • A1 Correct answer: 9.

Question 2

(a) 192\frac{19}{2}

  • M1 Average the middle pair of the lower half.
  • M1 Average the middle pair of the upper half, then subtract Q1.
  • A1 Correct answer: 192\frac{19}{2}

(b) 212\frac{21}{2}

  • M1 An even number of observations has two central values.
  • A1 Correct answer: 212\frac{21}{2}

Question 3

(a) 29

  • P1 Establishing 9×189\times 18 or an equivalent valid method.
  • P1 Establishing 162−(4×6+2×22+36)162-(4\times 6+2\times 22+36) or an equivalent valid method.
  • P1 Establishing 58/258/2 or an equivalent valid method.
  • C1 Correct conclusion with the complete supporting argument: 29

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Box plots and distribution comparisons

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