The back-to-back stem-and-leaf plot below shows the ages of patients seen by two doctors in a family clinic in one day. Compare the ages of the patients of doctor 1 and doctor 2 using the mean and the median of each data set.

Doctor 1 Doctor 2
| 3 | 5
9 2 0 | 2 | 0 0 2 3 6
8 7 5 | 1 | 3 7
9 7 3 2 1 1| 0 | 2 2 3 9
Key: means 29 9|2|3 means 23

Doctor 2. has the range of ages that far exceeds the range of Doctor1.

The mean of Doctor 1 is 13, and the median is 14. The mean of Doctor 2 is 15 and the median is 15.5.

No it's not....

The mean and median for doc 1 is 12, the mean for doc 2 is 16, the median for doc 2 is 18.5. How did you even get those numbers...

To compare the ages of the patients of doctor 1 and doctor 2 using the mean and the median, we need to calculate the mean and median for each data set.

Mean:
1. For doctor 1:
- Sum all the ages: 29 + 9 + 2 + 3 = 43
- Divide the sum by the number of data points: 43 / 4 = 10.75
- The mean age for doctor 1 is 10.75.

2. For doctor 2:
- Sum all the ages: 23 + 20 + 2 + 0 + 0 + 2 + 3 + 6 + 13 + 7 + 22 + 23 + 9 = 140
- Divide the sum by the number of data points: 140 / 13 ≈ 10.77 (rounded to two decimal places)
- The mean age for doctor 2 is approximately 10.77.

Median:
1. For doctor 1:
- Arrange the ages in ascending order: 2, 3, 9, 29
- Since there are 4 data points, the median is the average of the two middle values: (3 + 9) / 2 = 6
- The median age for doctor 1 is 6.

2. For doctor 2:
- Arrange the ages in ascending order: 0, 0, 2, 2, 2, 3, 6, 7, 9, 13, 20, 22, 23
- Since there are 13 data points, the median is the middle value: 7
- The median age for doctor 2 is 7.

Comparing the mean and median of each data set:
- For doctor 1, the mean age is 10.75, and the median age is 6.
- For doctor 2, the mean age is approximately 10.77, and the median age is 7.

Therefore, in terms of the mean age, the patients of doctor 1 have a slightly lower average age compared to doctor 2. However, in terms of the median age, the patients of doctor 1 have a lower median age compared to doctor 2.