1. **State the problem:** We are given the number of comments on 10 opinion articles: {15, 25, 10, 30, 20, 18, 22, 12, 28, 17}. Calculate the mean and standard deviation to analyze audience engagement consistency. 2. **Calculate the mean (average):** $$\text{mean} = \frac{15 + 25 + 10 + 30 + 20 + 18 + 22 + 12 + 28 + 17}{10}$$ $$= \frac{197}{10} = 19.7$$ The mean number of comments per article is 19.7. 3. **Calculate each deviation from the mean and square it:** $$ (15 - 19.7)^2 = (-4.7)^2 = 22.09 $$ $$ (25 - 19.7)^2 = 5.3^2 = 28.09 $$ $$ (10 - 19.7)^2 = (-9.7)^2 = 94.09 $$ $$ (30 - 19.7)^2 = 10.3^2 = 106.09 $$ $$ (20 - 19.7)^2 = 0.3^2 = 0.09 $$ $$ (18 - 19.7)^2 = (-1.7)^2 = 2.89 $$ $$ (22 - 19.7)^2 = 2.3^2 = 5.29 $$ $$ (12 - 19.7)^2 = (-7.7)^2 = 59.29 $$ $$ (28 - 19.7)^2 = 8.3^2 = 68.89 $$ $$ (17 - 19.7)^2 = (-2.7)^2 = 7.29 $$ 4. **Calculate variance:** Sum the squared deviations and divide by $n-1=9$ for sample standard deviation. $$ \text{variance} = \frac{22.09 + 28.09 + 94.09 + 106.09 + 0.09 + 2.89 + 5.29 + 59.29 + 68.89 + 7.29}{9} $$ $$ = \frac{393.10}{9} = 43.68 $$ 5. **Calculate standard deviation:** $$ \text{std deviation} = \sqrt{43.68} \approx 6.61 $$ 6. **Interpretation:** The mean of 19.7 comments shows average engagement, but a standard deviation of about 6.61 indicates a moderate spread in comments. This suggests the articles have varied performance in engagement—some articles get substantially more or fewer comments than average. If the news site aims for consistent engagement, they may want to investigate factors behind this variability and attempt to reduce it.