1. **State the problem:** Find the median of the set of numbers: 3, 4, 1, 1, 3, 4. 2. **Recall the definition of median:** The median is the middle value of a data set when the numbers are arranged in ascending order. If there is an even number of values, the median is the average of the two middle numbers. 3. **Arrange the numbers in ascending order:** $$1, 1, 3, 3, 4, 4$$ 4. **Identify the middle two numbers:** Since there are 6 numbers (even), the middle two are the 3rd and 4th numbers: $$3 \text{ and } 3$$ 5. **Calculate the median:** $$\text{Median} = \frac{3 + 3}{2} = \frac{6}{2} = 3$$ 6. **Conclusion:** The median of the set is **3**.