Question

Consider the following sets of sample data: A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312 B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

Answer 1

Dataset A

We have the following results:

`\bar X_A = 359.786`

`s_A= 60.904`

`CV_A = (60.904)/(359.786)= 0.169 \approx 0.2`

Dataset B

We have the following results:

`\bar X_B = 1.791`

`s_B= 0.635`

`CV_B = (0.635)/(1.791)= 0.355 \approx 0.4`

Explanation:

For this case we have the following info given:

A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312

B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41

We need to remember that the coeffcient of variation is given by this formula:

`CV= (s)/(\bar X)`

Where the sample mean is given by:

`\bar X= (\sum_(i=1)^n X_i)/(n)`

And the sample deviation given by:

`s=\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}`

Dataset A

We have the following results:

`\bar X_A = 359.786`

`s_A= 60.904`

`CV_A = (60.904)/(359.786)= 0.169 \approx 0.2`

Dataset B

We have the following results:

`\bar X_B = 1.791`

`s_B= 0.635`

`CV_B = (0.635)/(1.791)= 0.355 \approx 0.4`