Arrange the data sets below in increasing order of their coefficients of…
2024
Arrange the data sets below in increasing order of their coefficients of variation.
(A) standard deviation = 3.7, mean = 20
(B) standard deviation = 4.3, mean = 25
(C) standard deviation = 5.2, mean = 35
(D) standard deviation = 6.1, mean = 40
Choose the correct answer.
Answer: C. (C), (D), (B), (A) — ConceptThe coefficient of variation compares relative dispersion across data sets with different means. For a positive mean, CV = (standard deviation / mean)…
- A.
(A), (B), (C), (D)
- B.
(B), (C), (D), (A)
- C.
(C), (D), (B), (A)
- D.
(D), (C), (A), (B)
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
The coefficient of variation compares relative dispersion across data sets with different means. For a positive mean, CV = (standard deviation / mean) × 100%. Therefore, increasing CV means arranging the ratios standard deviation / mean from smallest to largest.
Application
Compute the coefficient of variation for each data set:
For A: (3.7 / 20) × 100 = 18.5%.
For B: (4.3 / 25) × 100 = 17.2%.
For C: (5.2 / 35) × 100 ≈ 14.86%.
For D: (6.1 / 40) × 100 = 15.25%.
Cross-check
Without relying on rounded percentages, cross-multiplication confirms each adjacent comparison: 5.2 × 40 = 208 < 6.1 × 35 = 213.5; 6.1 × 25 = 152.5 < 4.3 × 40 = 172; and 4.3 × 20 = 86 < 3.7 × 25 = 92.5.
Thus 14.86% < 15.25% < 17.2% < 18.5%, so the required increasing order is (C), (D), (B), (A).