Question

The number of hours worked by the employees of Bob's Car Wash in one week are listed.
20, 40, 30, 36, 36, 40, 39, 36, 38
The mean is 35 hours per week and the median is 36 hours per week.
Which statement best explains why the mean is less than the median?
• A. There are only 9 employees.
• B. Nobody works more than 40 hours.
C. The smallest number is half the largest.
D. One worker works much fewer hours than everyone else.

Answer 1

To determine why the mean (35 hours) is less than the median (36 hours), we should look for factors in the data that could skew the mean downwards.

Here are the hours worked by employees in ascending order:
20, 30, 36, 36, 36, 38, 39, 40, 40.

Given this data, we can see that there is one employee who works significantly fewer hours (20) compared to the others. This outlier can pull the mean down, leading to a situation where the mean is less than the median, especially since the median is based on the middle value(s) and is less affected by outliers.

Therefore, the best explanation from the provided options is:

**D. One worker works much fewer hours than everyone else.**