1. **State the problem:** We have 10 articles with comment counts: $\{15, 25, 10, 30, 20, 18, 22, 12, 28, 17\}$. We need to calculate the mean and standard deviation of these comments to understand audience engagement consistency. 2. **Calculate the mean (average):** $$\text{mean} = \frac{15 + 25 + 10 + 30 + 20 + 18 + 22 + 12 + 28 + 17}{10} = \frac{197}{10} = 19.7$$ 3. **Calculate each deviation from the mean and square it:** $$\begin{aligned} (15 - 19.7)^2 &= (-4.7)^2 = 22.09 \\ (25 - 19.7)^2 &= 5.3^2 = 28.09 \\ (10 - 19.7)^2 &= (-9.7)^2 = 94.09 \\ (30 - 19.7)^2 &= 10.3^2 = 106.09 \\ (20 - 19.7)^2 &= 0.3^2 = 0.09 \\ (18 - 19.7)^2 &= (-1.7)^2 = 2.89 \\ (22 - 19.7)^2 &= 2.3^2 = 5.29 \\ (12 - 19.7)^2 &= (-7.7)^2 = 59.29 \\ (28 - 19.7)^2 &= 8.3^2 = 68.89 \\ (17 - 19.7)^2 &= (-2.7)^2 = 7.29 \end{aligned}$$ 4. **Sum the squared deviations:** $$22.09 + 28.09 + 94.09 + 106.09 + 0.09 + 2.89 + 5.29 + 59.29 + 68.89 + 7.29 = 393.1$$ 5. **Calculate the variance (sample variance, dividing by $n-1=9$):** $$\text{variance} = \frac{393.1}{9} \approx 43.68$$ 6. **Calculate the standard deviation:** $$\text{standard deviation} = \sqrt{43.68} \approx 6.61$$ 7. **Interpretation:** The mean number of comments is about 19.7, with a standard deviation of 6.61. This indicates moderate variability in audience engagement across articles. Since the standard deviation is roughly one-third of the mean, engagement is somewhat inconsistent. The news site might want to investigate factors causing this variation to achieve more consistent engagement. **Final answers:** - Mean comments: $19.7$ - Standard deviation: $6.61$