1. **State the problem:** We are given the ages of 6 employees: 26, 38, 26, 29, 28, 39. We need to find the population standard deviation of these ages, rounded to two decimal places. 2. **Formula for population standard deviation:** $$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}$$ where $\sigma$ is the population standard deviation, $x_i$ are the data points, $\mu$ is the population mean, and $N$ is the population size. 3. **Calculate the mean $\mu$:** $$\mu = \frac{26 + 38 + 26 + 29 + 28 + 39}{6} = \frac{186}{6} = 31$$ 4. **Calculate each squared deviation $(x_i - \mu)^2$:** - $(26 - 31)^2 = (-5)^2 = 25$ - $(38 - 31)^2 = 7^2 = 49$ - $(26 - 31)^2 = 25$ - $(29 - 31)^2 = (-2)^2 = 4$ - $(28 - 31)^2 = (-3)^2 = 9$ - $(39 - 31)^2 = 8^2 = 64$ 5. **Sum the squared deviations:** $$25 + 49 + 25 + 4 + 9 + 64 = 176$$ 6. **Divide by population size $N=6$:** $$\frac{176}{6} \approx 29.3333$$ 7. **Take the square root to find $\sigma$:** $$\sigma = \sqrt{29.3333} \approx 5.42$$ **Final answer:** The population standard deviation is approximately **5.42**.