1. **State the problem:** Find the population mean of the list of numbers: 20, 39, 31, 20, 25, 27, 22, 36, 14. 2. **Formula for population mean:** The population mean $\mu$ is given by $$\mu = \frac{\sum_{i=1}^N x_i}{N}$$ where $x_i$ are the data points and $N$ is the total number of data points. 3. **Count the number of data points:** There are $N=9$ numbers in the list. 4. **Sum the data points:** $$\sum_{i=1}^9 x_i = 20 + 39 + 31 + 20 + 25 + 27 + 22 + 36 + 14$$ Calculate the sum step-by-step: $$20 + 39 = 59$$ $$59 + 31 = 90$$ $$90 + 20 = 110$$ $$110 + 25 = 135$$ $$135 + 27 = 162$$ $$162 + 22 = 184$$ $$184 + 36 = 220$$ $$220 + 14 = 234$$ 5. **Calculate the mean:** $$\mu = \frac{234}{9}$$ Show cancellation: $$\mu = \frac{\cancel{234}}{\cancel{9}} = 26$$ 6. **Final answer:** The population mean of the list is $26$.