1. **Stating the problem:** We need to find the sum of the following numbers: 22.8, 25.8, 23.5, 20.7, 20.8, 24.7, 27, 22.5, 21, 28.5, 22.6, 24.5, 20.9, 18.9, 16.1, 19.5, 17.8, 22.6, 24.4, 17.6, 21.9, 22.6, 25.1, 18.7, 24.2, 23.1, 18.4, 21.1, 18.6, 18.3, 19.3, 22.8, 18.1, 15.4, 23.6, 21.2, 17.8, 16.8, 20.3, 18.6. 2. **Formula used:** To find the sum of a list of numbers, we use the formula: $$\text{Sum} = x_1 + x_2 + x_3 + \cdots + x_n$$ where $x_i$ are the numbers in the list. 3. **Calculation:** Adding all the numbers step-by-step: $$22.8 + 25.8 + 23.5 + 20.7 + 20.8 + 24.7 + 27 + 22.5 + 21 + 28.5 + 22.6 + 24.5 + 20.9 + 18.9 + 16.1 + 19.5 + 17.8 + 22.6 + 24.4 + 17.6 + 21.9 + 22.6 + 25.1 + 18.7 + 24.2 + 23.1 + 18.4 + 21.1 + 18.6 + 18.3 + 19.3 + 22.8 + 18.1 + 15.4 + 23.6 + 21.2 + 17.8 + 16.8 + 20.3 + 18.6 = 841.6$$ 4. **Explanation:** We simply add each number one by one to get the total sum. This is a straightforward addition problem. **Final answer:** $$\boxed{841.6}$$