1. **Stating the problem:** We are given a list of numbers and want to find the mean (average), median, and mode of the data set. 2. **Formula for mean:** The mean is calculated by summing all the numbers and dividing by the count of numbers. $$\text{Mean} = \frac{\sum x_i}{n}$$ 3. **Finding the mean:** Sum all numbers: $$9.8 + 9.2 + 10.4 + 8.1 + 20.1 + 23.0 + 18.4 + 4.6 + 12.7 + 9.2 + 14.7 + 9.8 + 17.3 + 11.5 + 15.0 + 13.8 + 16.1 + 9.2 + 27.6 + 13.2 + 5.0 + 9.0 + 8.1 + 7.0 + 9.0 = 320.3$$ Count of numbers $n = 25$ Calculate mean: $$\text{Mean} = \frac{320.3}{25} = 12.812$$ 4. **Finding the median:** Sort the numbers: $$4.6, 5.0, 7.0, 8.1, 8.1, 9.0, 9.0, 9.2, 9.2, 9.2, 9.8, 9.8, 10.4, 11.5, 12.7, 13.2, 13.8, 14.7, 15.0, 16.1, 17.3, 18.4, 20.1, 23.0, 27.6$$ Since $n=25$ is odd, median is the middle value at position $\frac{25+1}{2} = 13$ The 13th number is $10.4$ 5. **Finding the mode:** Count frequency of each number: - 9.2 appears 3 times - 9.0 appears 2 times - 8.1 appears 2 times - 9.8 appears 2 times Others appear once Mode is the number with highest frequency: $9.2$ **Final answers:** - Mean = $12.812$ - Median = $10.4$ - Mode = $9.2$