Question

Suzanne owns a small business that employs 5 other people. Suzanne makes $100,000 per year, and the other 5 employees make between $40,000 and $50,000 per year.

Suzanne decides to increase her salary by $30,000 per year and leave the rest of the salaries the same.
How will increasing her salary affect the mean and median?

A: Both the mean and median will increase.
B: The mean will increase, the median will stay the same.
C: The median will increase, the mean will stay the same.
D: The mean will increase and the median will decrease.

Answer 1

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Explanation:

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Answer 2

B: The mean will increase, the median will stay the same.

Explanation:

According to the problem, the initial data set is

$40,000 $50,000 $100,000.

At this point the median is $50,000, because the median is define as the central value of the data set.

The median is

`x=(40000+50000+100000)/(3)=(190000)/(3)\approx 63,333.33`

After the Suzanne's salary increase, the data set is

$40,000 $50,000 $130,000.

The median after the increase is the same $50,000, because it represents the central value after the salary increase.

The median is

`x=(40000+50000+130000)/(3)\approx 73,333.33`

As you can observe, the median remains the same, but the mean increases.

Therefore, the right answer is B.