The salaries of the employees at a company are shown below. Which statement is true about the data set?

Question

$40,000   $45,000   $48,000   $52,000  $48,000  $46,000   $37,000   $45,000    $90,000   $42,000

 

MULTIPLE CHOICE

A. The salary of $37,000 causes the median to be lower than the mean

B. The salary of $37,000 causes the mean to be lower than the median

C. The salary of $90,000 causes the median to be greater than the mean

D. The salary of $90,000 causes the mean to be greater than the median

Answer 1

To answer this it’s best to order the data:

$37,000, $40,000, $42,000, $45,000, $45,000, $46,000, $48,000, $48,000, $52,000, $90,000

Median is $45,500 (central value) and mean (average) is $49,300.

The median is lower than the mean.

If the lowest salary is removed, the median is $46,000 and the mean is $50,666.67, and the median is still lower than the mean.

If the highest salary is removed, the median is $45,000 and the mean is $44,777.78, and the median is higher than the mean.

The highest salary causes the mean to be higher than the median, answer D. This shows that the higher outlier has a greater effect on the mean than the lower outlier.