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Grade 10 · Statistics
Statistics: Five-Number Summary & Box Plots (Grade 10)
MEMORANDUM
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Mark
/ 17
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.
- 1The mean of 23, 31, 27, 35, 29 and x is 29. Solve for x.(3)(23 + 31 + 27 + 35 + 29 + x)/6 = 29 (1)
145 + x = 29 × 6 = 174 (1)
x = 174 − 145 = 29 (1)✓✓✓ (3) - 2Find the mean of 4, 8, 9, 11, 13.(2)45 ÷ 5 = 9✓✓ (2)
- 3Find the median of 3, 7, 9, 12, 15, 18.(2)(9 + 12) ÷ 2 = 10,5✓✓ (2)
- 4Find the mode of 2, 5, 5, 7, 9, 5.(1)5✓ (1)
- 5Find the range of 12, 15, 18, 20, 35.(1)35 − 12 = 23✓ (1)
- 6For 12, 15, 18, 20, 22, 25, 28, 30, 35 find Q₁, Q₂ and Q₃.(3)Q₁ = 16,5 · Q₂ = 22 · Q₃ = 29✓✓✓ (3)
- 7Using the box plot below of that summary, find the IQR.(1)29 − 16,5 = 12,5✓ (1)
- 8What does the line inside the box represent?(1)The median (Q₂)✓ (1)
- 9What fraction of the data lies inside the box?(1)The middle 50%✓ (1)
- 10A box plot has minimum 4, Q₁ = 9, median 14, Q₃ = 21 and maximum 30. Calculate the interquartile range, and state what fraction of the data lies inside the box.(2)IQR = 21 − 9 = 12; the box holds the middle 50%✓✓ (2)
TOTAL: 17 marks