1. **Stating the problem:** We are given a distribution and asked to calculate the mean using the relationship among mode, median, and mean. 2. **Recall the formula:** For moderately skewed distributions, the empirical relationship is: $$\text{Mean} = 3 \times \text{Median} - 2 \times \text{Mode}$$ This formula helps estimate the mean if mode and median are known. 3. **Identify mode and median:** - The mode is the value that appears most frequently. - The median is the middle value when data is ordered. 4. **From the data given, the mode is 5** (appears most frequently). 5. **Estimate the median:** Since the data is not fully numeric or ordered clearly, assume median is approximately 9 (from the middle of the data range). 6. **Calculate the mean using the formula:** $$\text{Mean} = 3 \times 9 - 2 \times 5 = 27 - 10 = 17$$ 7. **Final answer:** The estimated mean is **17**.