Question

Based on daily measurements, Bob's weight has a mean of 200 pounds with a standard deviation of 16 pounds, while Mary's weight has a mean of 125 pounds with a standard deviation of 10 pounds. Who has the smaller dispersion based on the coefficient of variation?
(A) Bob
(B) Mary
(C) They are the same
(D) All of the above

Answer 1

Answer:

(C) They are the same

Step-by-step explanation:

The coefficient of variation CV is given by the following formula:

$CV = \frac{\sigma}{\mu}$

In which $\sigma$ is the standard deviation and $\mu$ is the mean.

Bob's weight has a mean of 200 pounds with a standard deviation of 16 pounds

This means that $\sigma = 16, \mu = 200$.

So his coefficient of variation is

$CV = \frac{16}{200} = 0.08$

Mary's weight has a mean of 125 pounds with a standard deviation of 10 pounds.

This means that $\sigma = 10, \mu = 125$

So her coefficient of variation is

$CV = \frac{10}{125} = 0.08$

They have the same coefficient of variation, so the correct answer is.

(C) They are the same