Mean (M) and coefficient of variation (CV expressed as a percentage) of…
2025
Mean (M) and coefficient of variation (CV expressed as a percentage) of different datasets are given in A-D below. Compute the standard deviation of each dataset and arrange in ascending order.
A. M = 60, CV = 70/3
B. M = 80, CV = 6.25
C. M = 70, CV = 160/7
D. M = 90, CV = 40/9
Choose the correct answer from the options given below:
- A.
D, A, B, C
- B.
A, C, D, B
- C.
D, B, A, C
- D.
B, D, C, A
Show answer & explanation
Correct answer: C
The coefficient of variation (CV) expresses the standard deviation (SD) as a percentage of the mean: CV = (SD ÷ Mean) × 100. Rearranging this identity gives the working formula SD = Mean × (CV ÷ 100), which recovers the absolute standard deviation whenever the CV percentage and mean are known.
Dataset A: M = 60, CV = 70/3%. SD = 60 × (70/3) ÷ 100 = (60 × 70) ÷ (3 × 100) = 4200/300 = 14.
Dataset B: M = 80, CV = 6.25%. SD = 80 × 6.25 ÷ 100 = 500/100 = 5.
Dataset C: M = 70, CV = 160/7%. SD = 70 × (160/7) ÷ 100 = (70 × 160) ÷ (7 × 100) = 11200/700 = 16.
Dataset D: M = 90, CV = 40/9%. SD = 90 × (40/9) ÷ 100 = (90 × 40) ÷ (9 × 100) = 3600/900 = 4.
Arranging the four standard deviations in ascending order: D (4) < B (5) < A (14) < C (16), which is the sequence D, B, A, C.
As an independent check, dividing each computed SD back by its own mean and multiplying by 100 should approximately return the given CV. 14/60 × 100 ≈ 23.33% ≈ 70/3%; 5/80 × 100 = 6.25%; 16/70 × 100 ≈ 22.86% ≈ 160/7%; 4/90 × 100 ≈ 4.44% ≈ 40/9%. All four reproduce the given data, confirming the ascending sequence D, B, A, C.