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

Answer:

Dataset A

We have the following results:

$\bar X_A = 359.786$

$s_A= 60.904$

$CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2$

Dataset B

We have the following results:

$\bar X_B = 1.791$

$s_B= 0.635$

$CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4$

Step-by-step 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:

$CV= \frac{s}{\bar X}$

Where the sample mean is given by:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

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

Dataset A

We have the following results:

$\bar X_A = 359.786$

$s_A= 60.904$

$CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2$

Dataset B

We have the following results:

$\bar X_B = 1.791$

$s_B= 0.635$

$CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4$