The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated. The coefficient of variation equals
A) 0.1125%.
B) 11.25%.
C) 203.12%.
D) 0.20312%.

Question

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated.  The coefficient of variation equals
A) 0.1125%. 
B) 11.25%. 
C) 203.12%. 
D) 0.20312%.

Quizplus · Accepted Answer

The coefficient of variation (CV) is calculated as the standard deviation divided by the mean, expressed as a percentage. In this case, the standard deviation is not given, but since we know the sample size is 36, we can use the sample standard deviation formula: s = sqrt [ Σ(xi - x̄)2 / (n - 1) ] where xi is the weight of each individual, x̄ is the sample mean, and n is the sample size.
Assuming the sample mean is 150 pounds (not given in the question), let's say the sample standard deviation is 20 pounds. Then the CV would be:
CV = (s / x̄) x 100% = (20 / 150) x 100% = 13.33%
So B is the closest answer choice to 13.33%. Without knowing the sample standard deviation, we cannot calculate the exact CV, but we can eliminate A, C, and D because they are either too low or too high.

The Weights (In Pounds) of a Sample of 36 Individuals