1. **State the Problem:** We are given two sets of sentiment scores from two platforms and need to calculate variance and standard deviation for each. Then determine which platform shows more variability. 2. **Recall Definitions:** Variance measures average squared deviation from the mean. Standard deviation is the square root of variance. 3. **Calculate for Platform X:** Scores: $\{0.2, 0.4, -0.1, 0.5, 0.3\}$ - Mean: $\bar{x} = \frac{0.2+0.4-0.1+0.5+0.3}{5} = \frac{1.3}{5} = 0.26$ - Squared deviations: $$(0.2 - 0.26)^2 = 0.0036$$ $$(0.4 - 0.26)^2 = 0.0196$$ $$(-0.1 - 0.26)^2 = 0.1296$$ $$(0.5 - 0.26)^2 = 0.0576$$ $$(0.3 - 0.26)^2 = 0.0016$$ - Variance: $$s^2 = \frac{0.0036 + 0.0196 + 0.1296 + 0.0576 + 0.0016}{5 - 1} = \frac{0.212}{4} = 0.053$$ - Standard deviation: $$s = \sqrt{0.053} \approx 0.23$$ 4. **Calculate for Platform Y:** Scores: $\{-0.3, 0.7, -0.2, 0.6, 0.1\}$ - Mean: $\bar{y} = \frac{-0.3 + 0.7 - 0.2 + 0.6 + 0.1}{5} = \frac{0.9}{5} = 0.18$ - Squared deviations: $$(-0.3 - 0.18)^2 = 0.2304$$ $$(0.7 - 0.18)^2 = 0.2704$$ $$(-0.2 - 0.18)^2 = 0.1444$$ $$(0.6 - 0.18)^2 = 0.1764$$ $$(0.1 - 0.18)^2 = 0.0064$$ - Variance: $$s^2 = \frac{0.2304 + 0.2704 + 0.1444 + 0.1764 + 0.0064}{4} = \frac{0.828}{4} = 0.207$$ - Standard deviation: $$s = \sqrt{0.207} \approx 0.46$$ 5. **Compare Variability:** Platform Y has a higher variance and standard deviation ($0.207$ and $0.46$) than Platform X ($0.053$ and $0.23$). This means Platform Y's sentiment scores are more spread out or variable. 6. **Implication for Newsroom Strategy:** Greater variability in Platform Y implies more polarized sentiment which might require nuanced content strategies, rapid response to sentiment shifts, or targeted messaging. Platform X's lower variability suggests more consistent sentiment, possibly allowing for steadier messaging. **Final Answers:** - Platform X variance = 0.053, standard deviation = 0.23 - Platform Y variance = 0.207, standard deviation = 0.46 - Platform Y shows more variability in sentiment which could influence a newsroom to adopt more flexible, responsive social media strategies on that platform.