Arrange the following datasets in decreasing order of coefficient of…
2024
Arrange the following datasets in decreasing order of coefficient of variation.
Dataset | Mean (X̄) | Standard deviation (σ) |
|---|---|---|
A | 13.8 | 4.3 |
B | 12.7 | 3.8 |
C | 14.9 | 5.7 |
D | 14.1 | 4.7 |
Answer: C. (C), (D), (A), (B) — ConceptThe coefficient of variation compares relative dispersion by scaling the standard deviation to the mean. For a dataset with positive mean, CV = (σ /…
- A.
(A), (B), (C), (D)
- B.
(B), (C), (D), (A)
- C.
(C), (D), (A), (B)
- D.
(D), (A), (B), (C)
Show answer & explanation
Correct answer: C
Concept
The coefficient of variation compares relative dispersion by scaling the standard deviation to the mean.
For a dataset with positive mean, CV = (σ / X̄) × 100%. A larger CV means greater spread relative to the mean.
Application
For dataset A: CV = (4.3 / 13.8) × 100% ≈ 31.16%.
For dataset B: CV = (3.8 / 12.7) × 100% ≈ 29.92%.
For dataset C: CV = (5.7 / 14.9) × 100% ≈ 38.26%.
For dataset D: CV = (4.7 / 14.1) × 100% = 33.33%.
Cross-check
Comparing the ratios before multiplying by 100 gives the same order: 5.7/14.9 > 4.7/14.1 > 4.3/13.8 > 3.8/12.7.
Therefore, the decreasing order is (C), (D), (A), (B).