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.
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