1. **State the problem:** Find the median of the data set given by the stem-and-leaf plot. 2. **List the data:** The data values extracted from the stem-and-leaf plot are: 14, 17, 20, 21, 24, 30, 31, 41, 43, 45, 47, 49, 50, 51, 51, 55, 56, 64, 66. 3. **Count the data points:** There are 19 data points in total. 4. **Find the median position:** The formula for the median position when data is ordered is $$\frac{n+1}{2}$$ where $n$ is the number of data points. 5. **Calculate the median position:** $$\frac{19+1}{2} = \frac{20}{2} = 10$$ so the median is the 10th value in the ordered list. 6. **Identify the median value:** The 10th value in the ordered list is 45. **Final answer:** The median of the data set is **45**.