1. The problem is to find the mean (average) of the numbers: 34, 33, 32, 31, 40, 39, 45, 32, 30, 32. 2. The formula for the mean of a set of numbers is: $$\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of numbers}}$$ 3. First, sum all the numbers: $$34 + 33 + 32 + 31 + 40 + 39 + 45 + 32 + 30 + 32 = 348$$ 4. Count the total numbers, which is 10. 5. Now, calculate the mean: $$\text{Mean} = \frac{348}{10} = 34.8$$ 6. Therefore, the mean of the given numbers is 34.8.