Answer :

Answer:

The coefficient of variation is 72.66%

Step-by-step explanation:

Data : 3 , 5 , 12 , 3 , 2

We are given that The mean of the sample is 5.

Formula of standard deviation =[tex]\sigma = \sqrt{\frac{\sum(x-\bar{x})^2}{n}[/tex]

Substitute the values :

[tex]\sigma = \sqrt{\frac{(3-5)^2+(5-5)^2+(12-5)^2+(3-5)^2+(2-5)^2}{5}}=3.633[/tex]

Coefficient of variation=[tex]\frac{\sigma}{\mu} \times 100=\frac{3.633}{5} \times 100 =72.66\%[/tex]

Hence The coefficient of variation is 72.66%

akposevictor

The coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%

Recall:

  • Coefficient of variation = Standard deviation / mean x 100%

Given, the following data:

  • 3 , 5 , 12 , 3 , 2
  • Mean is given as: 5

We are not given the standard deviation.

First, find the standard deviation of the data set, using the formula, [tex]\mathbf{SD = \sqrt{\frac{\sum (x - \bar{x}) }{n} } }[/tex]

  • Thus:

SD = [tex]\sqrt{\frac{66}{5} } = \sqrt{13.2}[/tex]

SD = 3.633

Next, find the coefficient of variation:

Cov. = 3.633/5 x 100 = 72.7%

Therefore, the coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%

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