Answer
• CV for Data Set A: 30.0%
• CV for Data Set B: 13.3%
Explanation
The coefficient of variation (CV) can be calculated using the following formula:
[tex]CV=\frac{\sigma}{\mu}[/tex]where σ is the standard deviation of the sample and μ is the mean.
μ can be calculated by adding all the data given and divided against the number of values in the data.
• Data Set A
[tex]\mu_A=\frac{2.48+1.02+1.87+...+1.18+1.53+1.06}{14}=1.79[/tex]where the "..." represents every single value of the data set.
• Data Set B
[tex]\mu_B=\frac{97+134+139+...+113+99+129}{11}=125.73[/tex]Then, the formula to calculate σ is:
[tex]\sigma=\sqrt{\frac{\sum_^(x-\mu)^2}{n-1}}[/tex]where x represents each value of the data, and n the number of values in the data. For example, (x - μ)² for the first three values of data A would be:
[tex](2.48-1.79)^2=0.48[/tex][tex](1.02-1.79)^2=0.59[/tex][tex](1.82-1.79)^2=0.00[/tex]Then, we would have to add all those operations for every single value of that set of data, and then replace it in the formula. If we do so, the addition of those operations in Data Set A is:
[tex]\sigma_A=\sqrt{\frac{3.74}{14-1}}\approx0.54[/tex]Following the same procedure for Data Set B we get the first three values:
[tex](97-125.72)^2=825.84[/tex][tex](134-125.72)^2=68.56[/tex][tex](139-125.72)^2=176.36[/tex]Adding all the operations and calculating σ:
[tex]\sigma_B=\sqrt{\frac{2786}{11-1}}\approx16.69[/tex]Finally, calculating CV for each Data Set and multiplying it times 100%:
[tex]CV_A=\frac{0.53}{1.79}\times100\%\approx30.0\%[/tex][tex]CV_B=\frac{16.69}{125.73}\times100\%\approx13.3\%[/tex]