Question

In a survey, patients are asked how long they sat in their doctor's waiting area. The results for two doctors are shown below.

Doctor #1 (waiting time in minutes): 5, 10, 10, 15, 20, 20, 20, 100
Doctor #2 (waiting time in minutes): 10, 10, 10, 20, 20, 20, 25, 25
Based on the results, what is the best measure of center to compare the data, and how do the measures compare?

A.
The median is the best measure. The median waiting time for Doctor #1 is 7.5 minutes longer than for Doctor #2.

B.
The mean is the best measure. The mean waiting time for Doctor #2 is 2.5 minutes longer than for Doctor #1.

C.
The mean is the best measure. The mean waiting time for Doctor #1 is 7.5 minutes longer than for Doctor #2.

D.
The median is the best measure. The median waiting time for Doctor #2 is 2.5 minutes longer than for Doctor #1.

Answer 1

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:**
1. Ordered values: 5, 10, 10, 15, 20, 20, 20, 100
2. 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:**
1. Ordered values: 10, 10, 10, 20, 20, 20, 25, 25
2. The median position (4th and 5th values): (20 + 20) / 2 = 20

### Summary of Findings
- **Mean Waiting Times:**
- Doctor #1: 26.25 minutes
- Doctor #2: 16.25 minutes
- Difference: 26.25 - 16.25 = 10 minutes (Doctor #1 is longer)

- **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.**