Question

Question 14 of 14, Step 1 of 212/19CorrectConsider the following sets of sample data:A: 4.39.4.47.4.21. 3.86, 3.72, 3.64.3.77.4.60, 3.82, 4.87.3.94, 2.91, 4.88, 4.21B: 4.8.3.9.2.8. 3.8. 4.7. 1.7.3.6, 2.2.4.8.3.2. 1.9Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.AnswerHow to enter your answer (opens in new window)CV for Data Set :%CV for Data Set B:%

Answer 1

Given:

Given the two sample data:

A: 4.39, 4.47, 4.21, 3.86, 3.72, 3.64, 3.77, 4.60, 3.82, 4.87, 3.94, 2.91, 4.88, 4.21

B: 4.8.3.9.2.8. 3.8. 4.7. 1.7.3.6, 2.2.4.8.3.2. 1.9

Required: Coefficient of variation of data A and B

Step-by-step explanation:

First, find the CV of sample data A.

Find the mean.

`\begin{gathered} \bar{x}=(\sum x_i)/(n) \\ =(4.39+4.47+4.21+3.86+3.72+3.64+3.77+4.60+3.82+4.87+3.94+2.91+4.88+4.21)/(14) \\ =(57.29)/(14) \\ =4.092143 \end{gathered}`

Find the sum of squares.

`\begin{gathered} \text{ Sum of squares}=\sum(x_i-\bar{x})^2 \\ =3.738236 \end{gathered}`

Calculate the standard deviation.

`\begin{gathered} s=\sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}} \\ =\sqrt{(3.738236)/(14-1)} \\ =0.536243 \end{gathered}`

Coefficient of variation of sample data A is

`\begin{gathered} CV=\frac{s}{\bar{x}} \\ =(0.536243)/(4.092143) \\ =0.131 \\ =13.1\% \end{gathered}`

Now, find the coefficient of variation of sample data B.

Find the mean.

`\begin{gathered} \bar{x}=(\sum x_i)/(n) \\ =(4.8+3.9+2.8+3.8+4.7+1.7+3.6+2.2+4.8+3.2+1.9)/(11) \\ =(37.4)/(11) \\ =3.4 \end{gathered}`

Find the sum of squares.

`\begin{gathered} \text{ Sum of squares =}\sum(x_i-\bar{x})^2 \\ =13.04 \end{gathered}`

Calculate the standard deviation.

`\begin{gathered} s=\sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}} \\ =\sqrt{(13.04)/(11-1)} \\ =1.141928 \end{gathered}`

Calculate the coefficient of variation.

`\begin{gathered} CV=\frac{s}{\bar{x}} \\ =(1.141928)/(3.4) \\ =0.336 \\ =33.6\% \end{gathered}`

Final Answer: CV of Data Set A = 13.1%

CV of Data Set B = 33.6%