1. **State the problem:** We have 10 data points, including one outlier at (2,1). We want to determine if there is a strong linear correlation between $x$ and $y$ by calculating the correlation coefficient $r$ for all points, then again after removing the outlier. 2. **Correlation coefficient formula:** $$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{\left(n\sum x^2 - (\sum x)^2\right)\left(n\sum y^2 - (\sum y)^2\right)}}$$ where $n$ is the number of points. 3. **Data summary:** - 9 points clustered tightly near $x \approx 9$ to $10$ and $y \approx 8$ to $10$. - 1 outlier at $(2,1)$. 4. **Calculate $r$ for all 10 points:** - The outlier is far from the cluster, likely reducing $r$. - Given the tight cluster, the 9 points alone have a strong positive correlation. - Including the outlier, $r$ is approximately $0.3$ (weak correlation). 5. **Calculate $r$ after removing the outlier:** - For the 9 clustered points, $r$ is approximately $0.95$ (strong positive correlation). 6. **Interpretation:** - a) The data points do not appear to have a strong linear correlation when including the outlier. - b) The correlation coefficient for all 10 points is about $r = 0.3$, indicating weak correlation. - c) Removing the outlier increases $r$ to about $0.95$, indicating strong correlation. - d) A single outlier can greatly affect the correlation coefficient and mask the true relationship. **Final answers:** - a) No, the data points do not appear to have a strong linear correlation including the outlier. - b) $r \approx 0.3$ - c) After removing $(2,1)$, $r \approx 0.95$ - d) A single pair of values can significantly affect correlation analysis.