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In a scatterplot, two or more individuals may have identical scores, causing their data points to overlap perfectly. Researchers can visually indicate this overlap by offsetting the points slightly along the $$x$$-axis, printing the number of individuals in parentheses directly next to the point, or increasing the size or darkness of the point in proportion to the number of overlapping individuals.

Displaying Overlapping Points in Scatterplots

In a scatterplot, when multiple individuals have identical scores resulting in perfectly overlapping data points, which of the following is a common method used by researchers to visually indicate this overlap?

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