1. The problem is to find the mean (average) of the given data set: 11.9, 11.2, 12.6, 9.8, 24.5, 28.0, 22.4, 5.6, 15.4, 11.2, 17.9, 11.9, 21.0, 14.0, 18.2, 16.8, 19.6, 11.2, 33.6, 16.1, 5.0, 9.0, 9.8, 7.0, 9.0. 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 25 numbers. 4. Next, sum all the data points: $$11.9 + 11.2 + 12.6 + 9.8 + 24.5 + 28.0 + 22.4 + 5.6 + 15.4 + 11.2 + 17.9 + 11.9 + 21.0 + 14.0 + 18.2 + 16.8 + 19.6 + 11.2 + 33.6 + 16.1 + 5.0 + 9.0 + 9.8 + 7.0 + 9.0 = 399.3$$ 5. Now, calculate the mean: $$\text{Mean} = \frac{399.3}{25}$$ 6. Simplify the fraction: $$\text{Mean} = \cancel{\frac{399.3}{25}} = 15.972$$ 7. Therefore, the mean of the data set is approximately $15.97$.