1. **Problem Statement:** Given the mode and mean of a data set as $15x$ and $18x$ respectively, find the median of the data. 2. **Formula Used:** For moderately skewed data, the empirical relationship between mean, median, and mode is: $$\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median})$$ 3. **Substitute the given values:** $$18x - 15x = 3(18x - \text{Median})$$ 4. **Simplify the left side:** $$3x = 3(18x - \text{Median})$$ 5. **Divide both sides by 3:** $$x = 18x - \text{Median}$$ 6. **Rearrange to solve for Median:** $$\text{Median} = 18x - x = 17x$$ 7. **Final answer:** The median of the data is $17x$.