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

Answer 1

To determine which statements are true, we need to calculate the mean, median, and mode for both inpatient and outpatient employees' commute times.

**Data:**
- 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

**1. Calculate the Mean:**

**Inpatient:**
Sum = 16 + 8 + 9 + 10 + 11 + 14 + 16 + 17 + 20 + 10 + 13 + 10 + 25 = 16 + 8 = 24 + 9 = 33 + 10 = 43 + 11 = 54 + 14 = 68 + 16 = 84 + 17 = 101 + 20 = 121 + 10 = 131 + 13 = 144 + 10 = 154 + 25 = 179
Mean = 179 / 13 ≈ 13.77

**Outpatient:**
Sum = 19 + 7 + 13 + 22 + 12 + 16 + 12 + 11 + 10 + 17 + 12 + 8 + 26 = 19 + 7 = 26 + 13 = 39 + 22 = 61 + 12 = 73 + 16 = 89 + 12 = 101 + 11 = 112 + 10 = 122 + 17 = 139 + 12 = 151 + 8 = 159 + 26 = 185
Mean = 185 / 13 ≈ 14.23

**2. Calculate the Median:**
To calculate the median, we need to sort the data.

**Inpatient Sorted:** 8, 9, 10, 10, 10, 11, 13, 14, 16, 16, 17, 20, 25
Median = 14 (7th value of sorted list)

**Outpatient Sorted:** 7, 8, 10, 11, 12, 12, 12, 13, 16, 17, 19, 22, 26
Median = 12 (7th value of sorted list)

**3. Calculate the Mode:**
The mode is the number that appears most frequently.

**Inpatient:** The mode is 10 (appears 3 times).
**Outpatient:** The mode is 12 (appears 3 times).

**4. Identify Outliers:**
An outlier can be identified using the IQR (Interquartile Range) method, but for simplicity in this case, we can observe the data:

**Inpatient:** 25 seems high compared to the rest of the data.
**Outpatient:** 26 also seems high.

**Final Analysis:**
- Mean: Outpatient mean (14.23) is higher than Inpatient mean (13.77)
- Median: Inpatient median (14) is higher than Outpatient median (12)
- Mode: Both have the same frequency for their modes (3 occurrences) but they are different numbers.
- Both data sets have outliers (25 for Inpatient and 26 for Outpatient)

**Thus the true statement among the options given is:**
- Both data sets have an outlier.