1. The problem is to find the mean (average) of the given data set: 11.1, 10.4, 11.7, 9.1, 22.8, 26.0, 21.6, 5.2, 14.3, 10.4, 16.6, 11.1, 19.5, 13.0, 16.9, 15.6, 18.2, 10.4, 31.2, 15.0, 5.0, 9.0, 9.1, 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: $$11.1 + 10.4 + 11.7 + 9.1 + 22.8 + 26.0 + 21.6 + 5.2 + 14.3 + 10.4 + 16.6 + 11.1 + 19.5 + 13.0 + 16.9 + 15.6 + 18.2 + 10.4 + 31.2 + 15.0 + 5.0 + 9.0 + 9.1 + 7.0 + 9.0 = 367.3$$ 5. Now, calculate the mean: $$\text{Mean} = \frac{367.3}{25}$$ 6. Simplify the fraction: $$\text{Mean} = \cancel{\frac{367.3}{25}} = 14.692$$ 7. Therefore, the mean of the data set is approximately 14.69. This means if you evenly distribute all the values, each would be about 14.69.