To determine the best measure of center (mean or median) and compare the measures for both doctors, let's calculate the mean and median for the waiting times.
Doctor #1 (waiting times: 5, 10, 10, 15, 20, 20, 20, 100)
Mean Calculation: \[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{5 + 10 + 10 + 15 + 20 + 20 + 20 + 100}{8} = \frac{210}{8} = 26.25 \]
Median Calculation:
- Ordered values: 5, 10, 10, 15, 20, 20, 20, 100
- The median position (4th and 5th values): (15 + 20) / 2 = 17.5
Doctor #2 (waiting times: 10, 10, 10, 20, 20, 20, 25, 25)
Mean Calculation: \[ \text{Mean} = \frac{10 + 10 + 10 + 20 + 20 + 20 + 25 + 25}{8} = \frac{130}{8} = 16.25 \]
Median Calculation:
- Ordered values: 10, 10, 10, 20, 20, 20, 25, 25
- The median position (4th and 5th values): (20 + 20) / 2 = 20
Summary of Findings
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Mean Waiting Times:
- Doctor #1: 26.25 minutes
- Doctor #2: 16.25 minutes
- Difference: 26.25 - 16.25 = 10 minutes (Doctor #1 is longer)
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Median Waiting Times:
- Doctor #1: 17.5 minutes
- Doctor #2: 20 minutes
- Difference: 20 - 17.5 = 2.5 minutes (Doctor #2 is longer)
Conclusion
- The median is often a better measure of center when dealing with skewed data or outliers. In this case, Doctor #1 has an outlier (100 minutes) that raises the mean significantly.
- Therefore, the best choice of the answer options is:
D. The median is the best measure. The median waiting time for Doctor #2 is 2.5 minutes longer than for Doctor #1.
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