Arrange the datasets with following pairs of mean (x̄) and standard deviation…
2024
Arrange the datasets with following pairs of mean (x̄) and standard deviation (σ) in increasing order of their coefficient of variation.
A. x̄ = 14, σ = 2.8
B. x̄ = 9, σ = 1.5
C. x̄ = 12, σ = 2.1
D. x̄ = 8, σ = 1.2
- A.
A, B, C, D
- B.
B, C, D, A
- C.
D, B, C, A
- D.
C, D, A, B
Show answer & explanation
Correct answer: C
The coefficient of variation (CV) is a relative measure of dispersion, defined as CV = σ / x̄ (standard deviation divided by mean), often expressed as a percentage. Because it is a ratio rather than an absolute value, it lets us compare the relative variability of datasets that have different means, which comparing raw standard deviations directly cannot do.
Dataset A: CV = σ / x̄ = 2.8 / 14 = 0.2 (20%)
Dataset B: CV = 1.5 / 9 ≈ 0.167 (16.7%)
Dataset C: CV = 2.1 / 12 = 0.175 (17.5%)
Dataset D: CV = 1.2 / 8 = 0.15 (15%)
Arranging these coefficients of variation in increasing order: D (0.15) < B (0.167) < C (0.175) < A (0.2), i.e., D, B, C, A.
Cross-check by comparing each adjacent pair through cross-multiplication, which avoids any rounding error from the decimal values:
D vs B: 1.2 × 9 = 10.8 and 1.5 × 8 = 12, so 1.2/8 < 1.5/9, i.e., D < B.
B vs C: 1.5 × 12 = 18 and 2.1 × 9 = 18.9, so 1.5/9 < 2.1/12, i.e., B < C.
C vs A: 2.1 × 14 = 29.4 and 2.8 × 12 = 33.6, so 2.1/12 < 2.8/14, i.e., C < A.
All three cross-multiplication checks agree with the direct computation, confirming the increasing order D, B, C, A.