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Grade 10 · Statistics
Statistics: Five-Number Summary & Box Plots (Grade 10)
MEMORANDUM
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  / 18

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Find the mean of 4, 8, 9, 11, 13.
    (2)
    45 ÷ 5 = 9✓✓ (2)
  2. 2
    Find the median of 3, 7, 9, 12, 15, 18.
    (2)
    (9 + 12) ÷ 2 = 10,5✓✓ (2)
  3. 3
    Find the mode of 2, 5, 5, 7, 9, 5.
    (2)
    5✓✓ (2)
  4. 4
    Find the range of 12, 15, 18, 20, 35.
    (2)
    35 − 12 = 23✓✓ (2)
  5. 5
    For 12, 15, 18, 20, 22, 25, 28, 30, 35 find Q₁, Q₂ and Q₃.
    (2)
    12min16.5Q₁22Q₂29Q₃35maxIQR = Q₃ − Q₁ = 29 − 16.5 = 12.5
    Q₁ = 16,5 · Q₂ = 22 · Q₃ = 29✓✓ (2)
  6. 6
    Using that summary, find the IQR.
    (2)
    12min16.5Q₁22Q₂29Q₃35maxIQR = Q₃ − Q₁ = 29 − 16.5 = 12.5
    29 − 16,5 = 12,5✓✓ (2)
  7. 7
    What does the line inside the box represent?
    (2)
    The median (Q₂)✓✓ (2)
  8. 8
    What fraction of the data lies inside the box?
    (2)
    The middle 50%✓✓ (2)
  9. 9
    A box plot has a much longer right whisker. Describe the skewness.
    (2)
    Skewed to the right (positively skewed)✓✓ (2)
TOTAL: 18 marks
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