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

1 answer

To determine which statement is true, we need to analyze the given data sets for inpatient and outpatient employees.

Inpatient Commute Times:

  • Data: 16, 8, 9, 10, 11, 14, 16, 17, 20, 10, 13, 10, 25
  • Sorted: 8, 9, 10, 10, 10, 11, 13, 14, 16, 16, 17, 20, 25
  • Modal Value: The most frequent value is 10 (appears 3 times).
  • Median Value: The median is the middle value. There are 13 values, so the median is the 7th value: 13.
  • Mean Value: \[ \text{Mean} = \frac{8 + 9 + 10 + 10 + 10 + 11 + 13 + 14 + 16 + 16 + 17 + 20 + 25}{13} = \frac{ 8 + 9 + 10 + 10 + 10 + 11 + 13 + 14 + 16 + 16 + 17 + 20 + 25}{13} = \frac{ 8 + 9 + 10 + 10 + 10 + 11 + 13 + 14 + 16 + 16 + 17 + 20 + 25 }{13} \approx 15.08 \]

Outpatient Commute Times:

  • Data: 19, 7, 13, 22, 12, 16, 12, 11, 10, 17, 12, 8, 26
  • Sorted: 7, 8, 10, 11, 12, 12, 12, 13, 16, 17, 19, 22, 26
  • Modal Value: The most frequent values are 12 (appears 3 times).
  • Median Value: The median is the 7th value: 12.
  • Mean Value: \[ \text{Mean} = \frac{7 + 8 + 10 + 11 + 12 + 12 + 12 + 13 + 16 + 17 + 19 + 22 + 26}{13} = \frac{ 7 + 8 + 10 + 11 + 12 + 12 + 12 + 13 + 16 + 17 + 19 + 22 + 26}{13} \approx 14.38 \]

Comparing the Summary:

  • Mode:

    • Inpatient: 10
    • Outpatient: 12 (Inpatient does not have a higher mode.)

  • Median:

    • Inpatient: 13
    • Outpatient: 12 (Inpatient has a higher median.)

  • Mean:

    • Inpatient: ≈ 15.08
    • Outpatient: ≈ 14.38 (Inpatient has a higher mean.)

  • Outlier Check:

    • Inpatient: 25 could be an outlier (the rest are relatively clustered lower).
    • Outpatient: 26 could be an outlier (the rest are relatively clustered lower).

Both data sets could potentially have an outlier.

Conclusion:

The statements evaluated:

  1. The inpatient employees have a higher modal commute to work than outpatient employees. (False)
  2. The inpatient employees have a higher median commute to work than outpatient employees. (True)
  3. Both data sets have an outlier. (True)
  4. The inpatient employees have a higher mean commute to work than outpatient employees. (True)

The true statement among those choices is:

  • "The inpatient employees have a higher median commute to work than outpatient employees." (This is the only answer that is solely true without possible misinterpretation of context.)