Data Representation and Interpretation — O/L Mathematics

How do I practise Data Representation and Interpretation?

1 question with a worked solution

1. The marks of 9 students in a test are: 42, 55, 60, 65, 68, 72, 75, 80, 88. Find the median mark and the interquartile range (IQR).
   1. A) Median = 68, IQR = 15
   2. B) Median = 72, IQR = 20
   3. C) Median = 68, IQR = 20
   4. D) Median = 65, IQR = 18
   Check my answer

   Correct answer: C) Median = 68, IQR = 20

   Since n = 9, the median is the 5th value = 68. Lower half values: 42, 55, 60, 65 → Q₁ = (55 + 60)/2 = 57.5. Upper half values: 72, 75, 80, 88 → Q₃ = (75 + 80)/2 = 77.5. IQR = Q₃ - Q₁ = 77.5 - 57.5 = 20.

   Show worked solution

   Step 1: Data is already sorted in ascending order (n = 9). Step 2: Median position = (9 + 1)/2 = 5th term → Median = 68. Step 3: Lower quartile Q₁: median of first 4 values (42, 55, 60, 65) = (55 + 60)/2 = 57.5. Step 4: Upper quartile Q₃: median of last 4 values (72, 75, 80, 88) = (75 + 80)/2 = 77.5. Step 5: IQR = Q₃ - Q₁ = 77.5 - 57.5 = 20. Answer: Median = 68, IQR = 20.
   Modelled on: the O/L Mathematics examination pattern

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Where does Data Representation and Interpretation fit in the syllabus?

Grade 11 · Term 2