1. **State the problem:** Find the mean (average) of the numbers 1, 2, 2, 5, 6, 7, 8. 2. **Formula for the mean:** The mean of a set of numbers is given by $$\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of numbers}}$$ 3. **Calculate the sum:** Add all the numbers together: $$1 + 2 + 2 + 5 + 6 + 7 + 8 = 31$$ 4. **Count the numbers:** There are 7 numbers in total. 5. **Calculate the mean:** Substitute the sum and count into the formula: $$\text{Mean} = \frac{31}{7}$$ 6. **Simplify the fraction:** $$\frac{31}{7} \approx 4.43$$ 7. **Interpretation:** The mean of the numbers 1, 2, 2, 5, 6, 7, 8 is approximately 4.43. This value represents the average of the data set.