Which type of graph shows the strength and direction of a relationship between two variables?

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A scattergram, also known as a scatter plot, is specifically designed to display the strength and direction of the relationship between two quantitative variables. In a scattergram, each point represents an observation in the dataset, with one variable plotted along the x-axis and the other along the y-axis.

When analyzing the points, you can determine whether there is a positive relationship (as one variable increases, the other does too), a negative relationship (as one variable increases, the other decreases), or no relationship at all (the points are scattered without a discernible pattern). The closer the points are to forming a straight line, the stronger the relationship between the variables.

In contrast, a bar graph is typically used to compare the quantities of different categories, which does not allow for the analysis of relationships between variables. A line graph primarily shows trends over time for a single variable rather than a relationship between two variables. A histogram, meanwhile, focuses on the frequency distribution of a single variable rather than exploring how two variables interact. Therefore, the scattergram is uniquely suited to illustrating the relationship between two variables, making it the correct choice in this context.