Question

The ages (in years) and weights (in pounds) of all wide receivers for a football 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 weights =% (Round to one decimal place as needed.)

Answer 1

Answer:

The coefficient of variation for the weight and age are 5.9% and 10.6%.

Step-by-step explanation:

The coefficient of variation (CV) is well defined as the ratio of the standard deviation to the mean. It exhibits the degree of variation in association to the mean of the population.

The formula to compute the coefficient of variation is:

$CV=\frac{\sigma}{\mu}\times 100\%$

Here σ = standard deviation and µ = mean.

Compute the mean and standard deviations of the two data set in Excel using the following functions.

Mean=AVERAGE()

Standard deviation=STDEV.S()

Consider the Excel sheet attached.

The mean and standard deviation of weight are:

Mean = 202, Standard deviation = 11.87

And the mean and standard deviation of weight are:

Mean = 25.88, Standard deviation = 2.75

Compute the coefficient of variation for the weight as follows:

$CV_{weight}=\frac{\sigma}{\mu}\times 100\%$

              $=\frac{11.87}{202}\times 100\%\\\\=5.87624\\\\=5.9\%$

Compute the coefficient of variation for the age as follows:

$CV_{age}=\frac{\sigma}{\mu}\times 100\%$

              $=\frac{2.75}{25.88}\times 100\%\\\\=10.62597\\\\=10.6\%$

Thus, the coefficient of variation for the weight and age are 5.9% and 10.6%.