1. The problem is to find the mean (average) of the given data set: 10.2, 9.6, 10.8, 8.4, 21.0, 24.0, 20.8, 4.8, 13.2, 9.6, 15.3, 10.2, 18.0, 12.0, 15.6, 14.4, 16.8, 9.6, 28.8, 13.8, 5.0, 9.0, 8.4, 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: $$10.2 + 9.6 + 10.8 + 8.4 + 21.0 + 24.0 + 20.8 + 4.8 + 13.2 + 9.6 + 15.3 + 10.2 + 18.0 + 12.0 + 15.6 + 14.4 + 16.8 + 9.6 + 28.8 + 13.8 + 5.0 + 9.0 + 8.4 + 7.0 + 9.0 = 350.1$$ 5. Now, calculate the mean: $$\text{Mean} = \frac{350.1}{25}$$ 6. Simplify the fraction: $$\text{Mean} = \cancel{\frac{350.1}{25}} = 14.004$$ 7. Therefore, the mean of the data set is approximately 14.004. This means if you evenly distribute the total sum among all 25 data points, each would have a value of about 14.004.