Which type of display is most likely to reveal an association between variables $x$ and $y$?

• A. A pie chart of $x$
• B. A boxplot of $y$
• C. A scatterplot
• D. A histogram of $x$

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the goal is to reveal an association between two variables, x and y. This means we want to see how changes in one variable relate to changes in the other.
2. Step 2: Recognize that a pie chart and a histogram display the distribution of a single variable, not the relationship between two variables. A pie chart shows proportions of categories, and a histogram shows frequency distribution of numerical data.
3. Step 3: Note that a boxplot summarizes the distribution of one variable (like y) by showing its median, quartiles, and potential outliers, but it does not directly show how y relates to x.
4. Step 4: Identify that a scatterplot plots individual data points with x-values on the horizontal axis and y-values on the vertical axis, allowing us to visually assess any pattern, trend, or association between the two variables.
5. Step 5: Conclude that among the given options, the scatterplot is the most appropriate display to reveal an association between variables x and y because it directly shows their paired values and potential relationships.