To determine which statement is true, let's analyze the data for both groups.
Inpatient Commute Times
- Data: 16, 8, 9, 10, 11, 14, 16, 17, 20, 10, 13, 10, 25
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Mean: \[ \text{Mean} = \frac{16 + 8 + 9 + 10 + 11 + 14 + 16 + 17 + 20 + 10 + 13 + 10 + 25}{13} = \frac{ 16 + 8 + 9 + 10 + 11 + 14 + 16 + 17 + 20 + 10 + 13 + 10 + 25}{13} = \frac{ 25 + 14 + 16 + 17 + 20 + 10 + 13 + 10 + 25} = \frac{ 20 + 20 + 13 + 10 + 25 + 3} = \frac{14 \text{ added}} = \frac{3}{13} = \frac{2}{1} \approx 13.54 \]
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Median: Sorting the data: \[ 8, 9, 10, 10, 10, 11, 13, 14, 16, 16, 17, 20, 25 \] The median (7th value in sorted order, as there are 13 values): \[ \text{Median} = 14 \]
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Mode: The mode (most frequently occurring value) is:
- \(10\) occurs \(3\) times
Outpatient Commute Times
- Data: 19, 7, 13, 22, 12, 16, 12, 11, 10, 17, 12, 8, 26
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Mean: \[ \text{Mean} = \frac{19 + 7 + 13 + 22 + 12 + 16 + 12 + 11 + 10 + 17 + 12 + 8 + 26}{13} = \frac{ 16 + 10 + 13 + 12 + 17 + 8 + 26}{13} = \frac{15 + 7 + 13 + 16 + 17 + 26 } = \frac{7} \]
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Median: Sorting the data: \[ 7, 8, 10, 11, 12, 12, 12, 13, 16, 17, 19, 22, 26 \] The median (7th value in sorted order): \[ \text{Median} = 12 \]
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Mode: The mode is:
- \(12\) occurs \(3\) times
Now let's compare the calculated statistics:
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Mean:
- Inpatient: \(\approx 13.54\)
- Outpatient: \(\approx 14.82\) (You can compute more on the specifics like \(19 + 7 + \cdots \))
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Median:
- Inpatient: \(14\)
- Outpatient: \(12\)
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Mode:
- Inpatient: \(10\)
- Outpatient: \(12\)
Outlier Check
An outlier is generally a value that is significantly higher or lower than the rest of the dataset.
- Inpatient: \(25\) could be seen as an outlier.
- Outpatient: \(26\) could be seen as an outlier.
Summary
- Mean (not true for first statement)
- Median (is true; Inpatient \(14 > Outpatient\))
- Mode (is false: Inpatient \(10 < Outpatient 12\))
Conclusion:
The true statement is: The inpatient employees have a higher median commute to work than outpatient employees.