Find the coefficient of the given data sets 7,2,8,11,6,13,16
2025
Find the coefficient of the given data sets 7,2,8,11,6,13,16
Answer: D. 48.22 — Solution (population standard deviation assumed): Compute the mean: mean = (7 + 2 + 8 + 11 + 6 + 13 + 16) / 7 = 63 / 7 = 9. Compute squared deviations and…
- A.
48.64
- B.
43.34
- C.
42.34
- D.
48.22
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Correct answer: D
Solution (population standard deviation assumed):
Compute the mean: mean = (7 + 2 + 8 + 11 + 6 + 13 + 16) / 7 = 63 / 7 = 9.
Compute squared deviations and their sum: (7-9)^2 = 4, (2-9)^2 = 49, (8-9)^2 = 1, (11-9)^2 = 4, (6-9)^2 = 9, (13-9)^2 = 16, (16-9)^2 = 49; sum = 132.
Variance (population) = sum of squared deviations / n = 132 / 7 ≈ 18.857142857.
Standard deviation = sqrt(variance) = sqrt(18.857142857) ≈ 4.343064.
Coefficient of variation (%) = (standard deviation / mean) × 100 = (4.343064 / 9) × 100 ≈ 48.2563%.
Final answer: approximately 48.26% (rounded to two decimal places). Note: the value 48.22% in the original solution differs only by a small rounding of intermediate values (for example rounding the standard deviation to 4.34 gives 48.22%).