1. The problem is to find the mean (average) of the given data set: 7.500, 15.000, 7.500, 10.000, ..., 7.500. 2. The formula for the mean of a data set is: $$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$$ 3. First, count the number of data points. There are 60 numbers in the list. 4. Next, sum all the data points: $$7.5 + 15 + 7.5 + 10 + 10 + 10 + 10 + 15 + 10 + 10 + 7.5 + 10 + 10 + 15 + 10 + 10 + 10 + 7.5 + 10 + 7.5 + 7.5 + 7.5 + 10 + 10 + 10 + 7.5 + 7.5 + 10 + 7.5 + 10 + 7.5 + 10 + 10 + 7.5 + 10 + 10 + 10 + 10 + 10 + 10 + 7.5 + 7.5 + 7.5 + 7.5 + 10 + 10 + 10 + 10 + 10 + 15 + 7.5 + 7.5 + 7.5 + 10 + 10 + 7.5 + 7.5 + 15 + 10 + 7.5 + 10 + 7.5 + 7.5 + 7.5 + 7.5 + 7.5 + 7.5$$ 5. Calculate the sum: $$\text{Sum} = 570$$ 6. Now calculate the mean: $$\text{Mean} = \frac{570}{60}$$ 7. Simplify the fraction: $$\text{Mean} = \frac{\cancel{570}^{9.5 \times 60}}{\cancel{60}^{1 \times 60}} = 9.5$$ 8. Therefore, the mean of the data set is $9.5$. This means if all values were equal, each would be 9.5 to have the same total sum as the original data set.