1. **State the problem:** Calculate the mean of the data set: 7, 10, 13, 14, 22. 2. **Formula for the mean:** 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 of the data points:** $$7 + 10 + 13 + 14 + 22 = 66$$ 4. **Count the number of data points:** There are 5 data points. 5. **Calculate the mean:** $$\text{mean} = \frac{66}{5}$$ 6. **Simplify the fraction:** $$\text{mean} = \frac{\cancel{66}}{\cancel{5}} = 13.2$$ 7. **Final answer:** The mean of the data set is **13.2**.