1. **Stating the problem:** We are given a list of numbers and want to find the mean (average) of these values. 2. **Formula for the mean:** The mean of a set of numbers $x_1, x_2, \ldots, x_n$ is given by $$\text{mean} = \frac{\sum_{i=1}^n x_i}{n}$$ where $n$ is the number of values. 3. **Count the numbers:** There are 24 numbers in the list. 4. **Sum the numbers:** $$11.1 + 10.4 + 11.7 + 9.1 + 22.8 + 26.0 + 21.6 + 5.2 + 14.3 + 10.4 + 16.6 + 11.1 + 19.5 + 13.0 + 16.9 + 15.6 + 18.2 + 10.4 + 31.2 + 15.0 + 5.0 + 9.0 + 9.1 + 7.0 + 9.0$$ 5. **Calculate the sum:** $$\sum = 11.1 + 10.4 + 11.7 + 9.1 + 22.8 + 26.0 + 21.6 + 5.2 + 14.3 + 10.4 + 16.6 + 11.1 + 19.5 + 13.0 + 16.9 + 15.6 + 18.2 + 10.4 + 31.2 + 15.0 + 5.0 + 9.0 + 9.1 + 7.0 + 9.0 = 388.3$$ 6. **Apply the mean formula:** $$\text{mean} = \frac{388.3}{24}$$ 7. **Simplify the fraction:** $$\text{mean} = \frac{\cancel{388.3}}{\cancel{24}} = 16.1791667$$ 8. **Final answer:** The mean of the given numbers is approximately $$16.18$$