Question

A marina rents boat slips monthly as listed below:

$400, $350, $375, $325, $325, $350, $375, $275, $425, $320, $350, $475.

They decide to raise their rates by $45. How will this affect the mean and the standard deviation?

A) The mean and the standard deviation will remain the same.

B) The mean will increase, and the standard deviation will increase.

C) The mean will increase, and the standard deviation will decrease.

D) The mean will increase, and the standard deviation will remain the same.

Answer 1

Option D is correct.

Explanation:

We have been given the rate is raised by $45

`Mean=\frac{\text{sum of observations}}{\text{number of observations}}`

Since, if we increased mean by 45 there will be no change in number of observations and in sum because there is symmetry in the sum of observations.

So, mean will be increased by $45

And standard deviation will remain same because it means how far the term is from the mean.

Therefore, option D is correct.