1. **State the problem:** We are given the data set $\{6,8,11,14,17,19,25\}$ and need to find the median. 2. **Recall the definition of median:** The median is the middle value of a data set when the numbers are arranged in ascending order. 3. **Arrange the data in ascending order:** The data is already sorted: $6,8,11,14,17,19,25$. 4. **Count the number of data points:** There are 7 numbers. 5. **Find the middle position:** Since 7 is odd, the median is the value at position $\frac{7+1}{2} = 4$. 6. **Identify the median:** The 4th number in the ordered list is $14$. 7. **Conclusion:** The median of the data set is $14$.