1. The problem states that the mode is 400 and the median is 500, and we need to find the mean. 2. For a moderately symmetric distribution, the empirical relationship between mean, median, and mode is given by the formula: $$\text{Mean} = 3 \times \text{Median} - 2 \times \text{Mode}$$ 3. Substitute the given values into the formula: $$\text{Mean} = 3 \times 500 - 2 \times 400$$ 4. Calculate the values: $$\text{Mean} = 1500 - 800 = 700$$ 5. Therefore, the mean is 700.