Which of the following scatterplots best illustrates an outlier that is extreme in both the $x$- and $y$-direction?

• A. A scatterplot where most points form a linear pattern, but one point is far away from the cluster both horizontally ($x$-direction) and vertically ($y$-direction).
• B. A scatterplot where one point is far from the cluster only in the $y$-direction, but not in the $x$-direction.
• C. A scatterplot where all points are closely clustered along a straight line with no points far from the group.
• D. A scatterplot where one point is far from the cluster only in the $x$-direction, but not in the $y$-direction.

Answer: (A)

Verified step by step guidance

1. Understand what an outlier is: an outlier is a data point that differs significantly from other observations in the dataset.
2. Recognize that an outlier extreme in both the x- and y-direction means the point is far away from the main cluster horizontally (x-axis) and vertically (y-axis).
3. Visualize the scatterplots: identify which plot has a point that is distant from the main cluster in both directions, not just one.
4. Eliminate options where the outlier is only far in one direction (either x or y) or where all points are closely clustered with no outliers.
5. Conclude that the scatterplot best illustrating an outlier extreme in both directions is the one where most points form a linear pattern but one point is far away from the cluster both horizontally and vertically.