Which of the following scatterplots best shows an outlier in both the $x$- and $y$-direction?

• A. A scatterplot where most points are clustered near the center, but one point is far to the right and far above the main cluster.
• B. A scatterplot where one point is far above the main cluster but has a similar $x$-value as the other points.
• C. A scatterplot where all points are closely clustered along a straight line.
• D. A scatterplot where one point is far to the right but at the same vertical level as the main cluster.

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 a scatterplot, an outlier can be unusual in the x-direction (horizontal), the y-direction (vertical), or both.
2. Identify an outlier in the x-direction: this means the point is far away horizontally from the cluster of other points. It should have an x-value much larger or smaller than the rest.
3. Identify an outlier in the y-direction: this means the point is far away vertically from the cluster of other points. It should have a y-value much larger or smaller than the rest.
4. Look for a point that is an outlier in both directions simultaneously: this point will be far to the right or left (x-direction) and far above or below (y-direction) the main cluster of points.
5. Compare the descriptions of the scatterplots: the one that describes a point far to the right and far above the main cluster best represents an outlier in both x- and y-directions.