If you encounter a scatter plot on the TASC Math exam, you’ll probably be asked to show how the two variables in the chart are related to each other—or whether a relationship exists between them at all.

A scatter plot shows the relationship between two variables. When looking at a scatter plot, you look at the correlation, which gauges the strength of the relationship and the direction. This means a correlation can be strong or weak and can be positive, negative, or neither.

Examples of scatter plots.

Depending on the strength of the correlation, you can infer a trend in the relationship. The figure shown here illustrates some examples of scatter plots and the types of correlations that can appear. Notice how when there is a correlation, the points tend to line up in one direction.

A common example of a scatter plot is the relationship between people’s shoe sizes and their IQs. When a large data collection is analyzed, you see that there’s no correlation. If there were one, you could make a statement like “People with bigger shoe sizes are smarter.” However, there’s a wide range of IQs and shoe size combinations, and you can’t gauge a person’s intelligence based on his or her shoe size (no correlation).

Practice question

  1. What statement corresponds to the relationship illustrated by the following scatter plot?

    A. The longer you study, the worse you will do on the test. B. The longer you study, the better you will do on the test. C. The amount of time studying does not affect the score on the test. D. Not enough information can be gathered.

Answer and explanation

  1. The correct answer is Choice (B). Because the trend line, or line of best fit, of this scatter plot has a positive slope, there is a positive relationship between the variables. This means as one increases the other increases: the longer you study, the better you will do on the test, Choice (B) is correct. For there to be no relationship, the line of best fit would be a “flat” horizontal line. For a negative relationship, the slope would be negative or “pointing down.”

About This Article

This article is from the book:

About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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