Answer: C. The medians of data sets A and B are equal.

Explanation:1. **Understand the median:** The median is the middle value in a data set that has been ordered from least to greatest. If there is an even number of values, the median is the average of the two middle values.

2. **Determine the position of the median:** Both data sets have $11$ values. Since $11$ is an odd number, the median will be the single middle value. The position of the median is $\dfrac{n+1}{2}$, where $n$ is the number of values. Position = $\dfrac{11+1}{2} = \dfrac{12}{2} = 6$. So, the median is the $6^{th}$ value in each ordered data set.

3. **Find the median of Data set A:** Data set A is already ordered: $2, 2, 2, 5, 5, \underline{8}, 11, 11, 14, 14, 14$. The $6^{th}$ value is $8$. Median of Data set A = $8$.

4. **Find the median of Data set B:** Data set B is already ordered: $2, 5, 5, 8, 8, \underline{8}, 8, 8, 11, 11, 14$. The $6^{th}$ value is $8$. Median of Data set B = $8$.

5. **Compare the medians:** Median of Data set A ($8$) is equal to the Median of Data set B ($8$).

6. **Conclusion:** The medians of data sets A and B are equal.