Arrange the data sets with following pairs of mean (x’) and standard…
2024
Arrange the data sets with following pairs of mean (x’) and standard derivation (σ) in increasing order of their coefficient of variation. (Α) x’=8,σ=1.7
(Β) x’=11,σ=2.2
(C) x’=15,σ=3.6
(D) x’=16,σ=3
Choose the correct answer from the options given below:
- A.
(A), (B), (D), (C)
- B.
(B), (D), (C), (A)
- C.
(C), (B), (D), (A)
- D.
(D), (B), (A), (C)
Attempted by 16 students.
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Correct answer: D
Compute the coefficient of variation (CV = σ / mean) for each dataset:
Dataset with mean 8 and σ 1.7: CV = 1.7 ÷ 8 = 0.2125 = 21.25%
Dataset with mean 11 and σ 2.2: CV = 2.2 ÷ 11 = 0.20 = 20.00%
Dataset with mean 15 and σ 3.6: CV = 3.6 ÷ 15 = 0.24 = 24.00%
Dataset with mean 16 and σ 3: CV = 3 ÷ 16 = 0.1875 = 18.75%
Arrange the datasets in increasing order of CV (smallest to largest):
(mean 16, σ 3) — CV = 18.75%
(mean 11, σ 2.2) — CV = 20.00%
(mean 8, σ 1.7) — CV = 21.25%
(mean 15, σ 3.6) — CV = 24.00%
Final answer: The datasets arranged in increasing order of coefficient of variation are (mean 16, σ 3), (mean 11, σ 2.2), (mean 8, σ 1.7), (mean 15, σ 3.6).
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