1. **State the problem:** Find the mean (average) of the data set: 12, 13, 17, 17, 19, 23, 27, 29, 31, 34, 34. 2. **Formula:** The mean is calculated by summing all the values and dividing by the number of values. $$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$$ 3. **Calculate the sum:** $$12 + 13 + 17 + 17 + 19 + 23 + 27 + 29 + 31 + 34 + 34 = 256$$ 4. **Count the number of data points:** There are 11 numbers in the data set. 5. **Calculate the mean:** $$\text{Mean} = \frac{256}{11}$$ 6. **Simplify the fraction:** $$\text{Mean} = \frac{\cancel{256}}{\cancel{11}} = 23.27$$ (rounded to two decimal places) 7. **Final answer:** The mean of the data set is approximately $23.27$.