Measures of relative position — A/L Combined Mathematics

How do I practise Measures of relative position?

1 question with a worked solution

Check before you answer: Grouped Quartile Formulae: Identifying quartile classes from cumulative frequencies and applying the interpolation formula using lower boundaries.

1. In a dataset of examination marks, the lower quartile is Q₁ = 45 and the upper quartile is Q₃ = 75. What are the Interquartile Range (IQR) and the Semi-interquartile Range (Quartile Deviation)?
   1. A) IQR = 15, Quartile Deviation = 30
   2. B) IQR = 30, Quartile Deviation = 15
   3. C) IQR = 120, Quartile Deviation = 60
   4. D) IQR = 30, Quartile Deviation = 30
   Check my answer

   Correct answer: B) IQR = 30, Quartile Deviation = 15

   Interquartile Range is defined as IQR = Q₃ - Q₁ = 75 - 45 = 30. The Semi-interquartile Range (Quartile Deviation) is half of IQR: QD = (Q₃ - Q₁) / 2 = 30 / 2 = 15.

   Show worked solution

   Step 1: IQR = Q₃ - Q₁ = 75 - 45 = 30. Step 2: Semi-IQR = IQR / 2 = 30 / 2 = 15. Answer: IQR = 30, Quartile Deviation = 15.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Measures of relative position fit in the syllabus?

Year 2 · Term 3