Asked by Vanessa Pressat on Apr 23, 2024
Verified
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%.
Coefficient of Variation
A standardized measure of the dispersion of a probability distribution or frequency distribution.
Weights
Quantitative values assigned to elements of a set as a measure of their importance or influence in statistical calculations.
- Comprehend the principle and computation of the coefficient of variation as an indicator of relative variability.
Verified Answer
AS
Amandeep Singh7 days ago
Final Answer :
B
Explanation :
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.
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.
Learning Objectives
- Comprehend the principle and computation of the coefficient of variation as an indicator of relative variability.
Related questions
The Coefficient of Variation (CV)provides a Relative Measure of the ...
Which of the Following Is One Way to Represent the ...
In the Formula for Calculating the Standard Deviation,what Does the ...
What Is the Formula for Calculating the Inclusive Range ...
In the Formula for Computing the Range,______ Is Used to ...