1. **Restate the problem:** Verify the calculation of the mean for the given data set. 2. **Recall the mean formula:** $$\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}$$ 3. **Count the data points:** There are $36$ data points. 4. **Sum the data values:** $$3 + 4 + 6 + 10 + 10 + 12 + 12 + 13 + 13 + 13 + 13 + 16 + 16 + 16 + 16 + 17 + 17 + 18 + 18 + 20 + 21 + 22 + 22 + 23 + 23 + 26 + 27 + 27 + 30 + 30 + 31 + 32 + 34 + 34 + 35 + 35 = 732$$ 5. **Calculate the mean:** $$\text{Mean} = \frac{732}{36}$$ 6. **Simplify the fraction:** $$\text{Mean} = 20.3333...$$ 7. **Round to the nearest tenth:** $$20.3$$ **Final answer:** The mean is correctly calculated as **20.3**.