What type of graph is most useful for illustrating the correlation between two variables?

A scatterplot is the most useful graph for illustrating the correlation between two variables because it allows for a visual representation of how one variable affects or relates to another. In a scatterplot, each point represents an observation in a two-dimensional space defined by both variables. By plotting the data points, you can easily observe patterns, trends, or relationships, such as whether the relationship is positive, negative, or non-existent.

This visual tool is especially effective in demonstrating linear and nonlinear correlations, making it easier to assess how closely the two variables are related. For instance, if the points cluster around a straight line, it indicates a strong correlation, whereas if the points are widely scattered, it suggests a weaker relationship.

In contrast, a bar graph is typically used to show categorical data and comparisons among discrete groups. A histogram focuses on the distribution of a single variable, indicating frequency rather than relationships. A pie chart is useful for illustrating proportions or percentages within a whole for categorical data, but it does not effectively show the relationship between two continuous variables. Thus, the scatterplot stands out as the ideal choice for correlation analysis.