1. **State the problem:** Calculate the mean of the data set: 126, 128, 140, 124, 140, 129. 2. **Formula for the mean:** The mean (average) is calculated by summing all the data points and dividing by the number of points. $$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$$ 3. **Calculate the sum:** $$126 + 128 + 140 + 124 + 140 + 129 = 787$$ 4. **Count the number of data points:** There are 6 data points. 5. **Calculate the mean:** $$\text{Mean} = \frac{787}{6}$$ 6. **Show cancellation for division:** $$\text{Mean} = \frac{\cancel{787}}{\cancel{6}}$$ (no common factors to cancel, so proceed to division) 7. **Divide:** $$\text{Mean} = 131.1666...$$ 8. **Round to the nearest tenth:** $$\text{Mean} \approx 131.2$$ **Final answer:** The mean of the data set is **131.2**.