The ages (in years) and heights (in inches) of all pitchers for a baseball team are listed. Find the coefficient of variation for each of the two data sets. Then compare the results. :: Click the icon to view the data sets. CV neights % (Round to one decimal place as needed.)

CV calculation for Height (inches)

The sample size is $n = 12$. We need to compute the sample mean $\bar X$ and sample variance $s^2$ are shown in the table below:

The sample mean $\bar X$ is computed as follows:

$\bar X = \frac{1}{n} \sum_{i=1}^n X_i = \frac{ 922}{ 12} = 76.833$

Also, the sample variance $s^2$ is

$s^2 = \frac{ 1}{n-1}\left(\sum_{i=1}^n X_i^2 - \frac{1}{n}\left(\sum_{i=1}^n X_i\right)^2 \right) = \frac{ 1}{ 12-1}\left( 70876 - \frac{ 922^2}{ 12} \right) = 3.242$

Therefore, the sample standard deviation $s$ is

$s = \sqrt{s^2} = \sqrt{ 3.242} = 1.801$

Now,

We all know that Coefficient of variation , CV is

$C{V}_{heights} = \frac{1.801}{76.833}\times 100 = 2.344\%$