1. The problem asks to calculate the mean and standard deviation of the number of comments for 10 opinion articles: {15, 25, 10, 30, 20, 18, 22, 12, 28, 17}. 2. First, calculate the mean (average) number of comments: $$ \text{mean} = \frac{15 + 25 + 10 + 30 + 20 + 18 + 22 + 12 + 28 + 17}{10} $$ $$ = \frac{197}{10} = 19.7 $$ 3. Next, calculate each deviation from the mean, square them, and find their average (variance): $$ (15-19.7)^2 = 22.09 $$ $$ (25-19.7)^2 = 28.09 $$ $$ (10-19.7)^2 = 94.09 $$ $$ (30-19.7)^2 = 106.09 $$ $$ (20-19.7)^2 = 0.09 $$ $$ (18-19.7)^2 = 2.89 $$ $$ (22-19.7)^2 = 5.29 $$ $$ (12-19.7)^2 = 59.29 $$ $$ (28-19.7)^2 = 68.89 $$ $$ (17-19.7)^2 = 7.29 $$ 4. Sum these squared deviations: $$ 22.09 + 28.09 + 94.09 + 106.09 + 0.09 + 2.89 + 5.29 + 59.29 + 68.89 + 7.29 = 393.99 $$ 5. Calculate the variance by dividing the sum by the number of data points (use population formula here for the whole sample): $$ \text{variance} = \frac{393.99}{10} = 39.399 $$ 6. Find the standard deviation by taking the square root of variance: $$ \text{standard deviation} = \sqrt{39.399} \approx 6.28 $$ 7. Interpretation: The mean is 19.7 comments per article, and the standard deviation 6.28 indicates moderate variability around this average. 8. Since the standard deviation is about 32% of the mean, there is some inconsistency in engagement among articles. Some articles have noticeably fewer or more comments, showing variation in audience interest. Final answer: Mean = 19.7, Standard deviation = 6.28. These statistics suggest that while the average engagement is around 20 comments, there is a moderate spread in audience responses, implying inconsistent engagement across the articles.