Question

Employees from two hospital departments, inpatient and outpatient, were selected at random. They were asked how many minutes it takes them to commute to work. The data are as follows.

Inpatient: 16, 8, 9, 10, 11, 14, 16, 17, 20, 10, 13, 10, 25
Outpatient: 19, 7, 13, 22, 12,16, 12, 11, 10, 17, 12, 8, 26

Which of the following statements is true?

(1 point)
Responses

The inpatient employees have a higher mean commute to work than outpatient employees.
The inpatient employees have a higher mean commute to work than outpatient employees.

The inpatient employees have higher modal commute to work than outpatient employees.
The inpatient employees have higher modal commute to work than outpatient employees.

Both data sets have an outlier.
Both data sets have an outlier.

The inpatient employees have a higher median commute to work than outpatient employees.

Answer 1

The true statement is: The inpatient employees have a higher median commute to work than outpatient employees.

Work:
- Inpatient sorted: 8,9,10,10,10,11,13,14,16,16,17,20,25 → median = 13.
- Outpatient sorted: 7,8,10,11,12,12,12,13,16,17,19,22,26 → median = 12.

Checks of the other claims:
- Means: inpatient mean = 179/13 ≈ 13.77, outpatient mean = 185/13 ≈ 14.23 → outpatient mean is higher.
- Modes: inpatient mode = 10, outpatient mode = 12 → inpatient mode is not higher.
- Outliers (IQR rule): inpatient fences are ~0.25 and 26.25 (no outliers); outpatient upper fence = 25.5 so 26 is an outlier (only outpatient has an outlier).