Measures of dispersion — A/L Combined Mathematics

How do I practise Measures of dispersion?

1 question with a worked solution

Check before you answer: Alternative Variance Formula: Applying σ² = (∑ f_i x_i² / N) - x̄² to compute variance efficiently without individual deviations.

1. For a sample of n = 5 observations {2, 4, 6, 8, 10}, what is the population variance (σ²)?
   1. A) 10.0
   2. B) 6.0
   3. C) 2.83
   4. D) 8.0
   Check my answer

   Correct answer: D) 8.0

   Mean μ = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6. Deviations from mean: (2-6)=-4, (4-6)=-2, (6-6)=0, (8-6)=2, (10-6)=4. Squared deviations: 16, 4, 0, 4, 16. Sum of squares = 40. Variance σ² = ∑(x - μ)² / n = 40 / 5 = 8.0.

   Show worked solution

   Step 1: Calculate mean: μ = 30 / 5 = 6. Step 2: Sum of squared deviations: (-4)² + (-2)² + 0² + 2² + 4² = 40. Step 3: Variance σ² = 40 / 5 = 8.0. Answer: 8.0.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Measures of dispersion fit in the syllabus?

Year 2 · Term 3