Ask a New Question
Menu

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

1 answer

To determine which statement is true, we need to analyze the data sets for both inpatient and outpatient employees. Here are the steps:

Inpatient Commute Times:

Data: 16, 8, 9, 10, 11, 14, 16, 17, 20, 10, 13, 10, 25

  1. Mode: The mode is the number that appears most frequently.

    • The values 10 and 16 appear 3 times each.
    • Mode = 10 and 16 (inpatient has two modes)

  2. Mean: The mean is the average of the data.

    • Mean = (16 + 8 + 9 + 10 + 11 + 14 + 16 + 17 + 20 + 10 + 13 + 10 + 25) / 13
    • Mean = 15.38 (approximately)

  3. Median: The median is the middle value when the data is ordered.

    • Ordered data: 8, 9, 10, 10, 10, 11, 13, 14, 16, 16, 17, 20, 25
    • Median (7th term) = 13

Outpatient Commute Times:

Data: 19, 7, 13, 22, 12, 16, 12, 11, 10, 17, 12, 8, 26

  1. Mode: The mode is the number that appears most frequently.

    • The value 12 appears 3 times.
    • Mode = 12 (outpatient has one mode)

  2. Mean: The mean is the average of the data.

    • Mean = (19 + 7 + 13 + 22 + 12 + 16 + 12 + 11 + 10 + 17 + 12 + 8 + 26) / 13
    • Mean = 15.31 (approximately)

  3. Median: The median is the middle value when the data is ordered.

    • Ordered data: 7, 8, 10, 11, 12, 12, 12, 13, 16, 17, 19, 22, 26
    • Median (7th term) = 12

Summary:

  • Inpatient Mode: 10 and 16
  • Outpatient Mode: 12
  • Inpatient Mean: 15.38
  • Outpatient Mean: 15.31
  • Inpatient Median: 13
  • Outpatient Median: 12

Outliers:

  • Inpatient: There is a potential outlier at 25.
  • Outpatient: There is a potential outlier at 26.

Evaluation of Statements:

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

    • False (inpatient has modes 10 and 16 compared to outpatient's mode of 12).

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

    • True (15.38 > 15.31).

  3. Both data sets have an outlier.

    • True (both have one outlier based on inference above).

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

    • True (13 > 12).

Conclusion:

The true statements are:

  • The inpatient employees have a higher mean commute to work than outpatient employees.
  • Both data sets have an outlier.
  • The inpatient employees have a higher median commute to work than outpatient employees.

Since only one statement can be marked "true" in this case, choose based on your judgment of importance: typically, the mean or median would be more standard in analysis.

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