1. **Problem statement:** Calculate the arithmetic mean (average) of the monthly mean air temperatures given for each month of the year. 2. **Formula:** The arithmetic mean $\bar{x}$ of $n$ values $x_1, x_2, \ldots, x_n$ is given by: $$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$ 3. **Given data:** Jan: 0.0, Feb: -2.7, Mar: 4.0, Apr: 8.1, May: 12.5, Jun: 16.7, Jul: 17.0, Aug: 14.7, Sep: 14.0, Oct: 10.5, Nov: 3.2, Dec: -1.6 4. **Calculate the sum:** $$\sum_{i=1}^{12} x_i = 0.0 + (-2.7) + 4.0 + 8.1 + 12.5 + 16.7 + 17.0 + 14.7 + 14.0 + 10.5 + 3.2 + (-1.6)$$ Calculate stepwise: $$= 0.0 - 2.7 + 4.0 + 8.1 + 12.5 + 16.7 + 17.0 + 14.7 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= (-2.7 + 4.0) + 8.1 + 12.5 + 16.7 + 17.0 + 14.7 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= 1.3 + 8.1 + 12.5 + 16.7 + 17.0 + 14.7 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= 9.4 + 12.5 + 16.7 + 17.0 + 14.7 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= 21.9 + 16.7 + 17.0 + 14.7 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= 38.6 + 17.0 + 14.7 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= 55.6 + 14.7 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= 70.3 + 14.0 + 10.5 + 3.2 - 1.6$$ $$= 84.3 + 10.5 + 3.2 - 1.6$$ $$= 94.8 + 3.2 - 1.6$$ $$= 98.0 - 1.6 = 96.4$$ 5. **Calculate the mean:** $$\bar{x} = \frac{96.4}{12}$$ 6. **Simplify the fraction:** $$\bar{x} = \frac{\cancel{96.4}}{\cancel{12}} = 8.0333...$$ 7. **Round to one decimal place:** $$\bar{x} \approx 8.0$$ **Final answer:** Der Jahresdurchschnitt beträgt 8.0 °C.