1. **State the problem:** We are given the data set: 6, 7, 5, 4, 7, 8, 9, 7. We need to find the mean and the mode. 2. **Mean formula:** The mean (average) of a data set is given by $$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$$ 3. **Calculate the sum:** $$6 + 7 + 5 + 4 + 7 + 8 + 9 + 7 = 53$$ 4. **Count the number of data points:** There are 8 numbers in the data set. 5. **Calculate the mean:** $$\text{Mean} = \frac{53}{8}$$ Show intermediate cancellation: $$\frac{\cancel{53}}{\cancel{8}} = 6.625$$ 6. **Mode definition:** The mode is the number that appears most frequently in the data set. 7. **Find the mode:** The number 7 appears 3 times, more than any other number. **Final answers:** Mean = 6.625 Mode = 7