1. **State the problem:** Calculate the mean of the data set: 45, 54, 55, 58, 53, 54, 54, 55, 49. 2. **Formula for mean:** The mean (average) is calculated by summing all the numbers and dividing by the count of numbers. $$\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}$$ 3. **Calculate the sum:** $$45 + 54 + 55 + 58 + 53 + 54 + 54 + 55 + 49 = 477$$ 4. **Count the numbers:** There are 9 numbers in total. 5. **Calculate the mean:** $$\text{Mean} = \frac{477}{9} = 53$$ 6. **Interpretation:** The mean value of the data set is 53, which represents the average of all the numbers provided.