# 1. 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...

1. 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

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### 2 Answers

The monthly rent for the boat is noted to take the following values: $400, $350, $375, $325, $325, $350, $375, $275, $425, $320, $350, $475

If the rent is increased by $45 each month, the mean rent rises by $45.

The standard deviation of the rent is: `sqrt(sum_(n=1)^12 (x_n - A)^2)` where A is the mean rent. If there is a uniform increase in rent of $45 in all the months, the mean rent changes from `A_(old)` to `A_(old) + 45` . The standard deviation does not change as `x_(n(old)) - A_(old) = x_(n(old)) + 45 - A_(old) - 45` for all values of `x_n`

**The correct answer is option D.**

D)

This is a linear transformation. The distribution will remain the same, however the placement of the graph would be shifted. The transformation that does affect both is multiplication - so if they doubled their rates, then the standard deviation and the mean would change.

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