AP Statistics · Topic 5.1 · Unit 5

AP Stats 5.1: Scatterplots and Association

By Jude Wallis · Published

Topic 5.1 in the Fall 2026 AP Statistics course covers scatterplots. A scatterplot plots two quantitative variables from the same individuals, explanatory on the x-axis and response on the y-axis. You describe its association by form, direction, strength, and unusual features.

AP Statistics: Unit 5 (topics 5.1). Topic 5.1 (Graphical Representations Between Two Quantitative Variables) opens Unit 5 in the Fall 2026 CED, first exam May 2027. Unit 5 is 10 to 20 percent of the multiple-choice section.

What topic 5.1 covers

Topic 5.1 is the first topic in Unit 5, Regression Analysis, in the Fall 2026 AP Statistics framework. It moves you from one variable to two, using a bivariate quantitative data set: a collection of ordered pairs measured on the same individuals in a sample or population. Each pair records two quantitative variables for one individual, such as a car's age and its resale value.

You display that data with a scatterplot, which shows the relationship between the two variables one point at a time. The explanatory variable goes on the x-axis; it is the variable whose values you use to explain or predict the other. The response variable goes on the y-axis; it is the value you are trying to explain or predict. Choosing which variable is which is the first decision every regression question asks of you.

Describing an association: form, direction, strength, and unusual features

Once the plot is drawn, the AP course expects a four-part description of the association between the variables.

  • Form is the overall shape. It is either linear, following a straight-line pattern, or non-linear, following a curve.
  • Direction is positive or negative. A positive association means that as the explanatory variable increases, the response tends to increase; a negative association means that as the explanatory variable increases, the response tends to decrease.
  • Strength is how closely the points follow the general pattern, described as strong, moderate, or weak. The tighter the points cluster around the pattern, the stronger the association.
  • Unusual features are things that break the pattern, such as clusters of points or individual points that do not fit the general trend.

Write these in context, not as bare labels. The phrase tend to matters, because it signals that the pattern is a general tendency and not a guarantee for every individual.

Justifying claims and what comes next

A scatterplot is evidence. Topic 5.1 asks you to justify claims in context using what the plot reveals, such as arguing that two variables are associated because the points show a clear upward trend. Keep your language precise, because describing points as forming a line is not the same as explaining why a relationship is linear.

This topic sets up the rest of Unit 5. Once you can see a linear form, topic 5.2 measures its strength with the correlation coefficient, and topics 5.3 through 5.5 fit and interpret a line. See the Unit 5 overview for how the pieces connect. A scatterplot also warns you when a line would be the wrong tool, because a curved cloud of points should never be summarized with a straight line.

Identify the variables and describe an association

For 15 used sedans, an analyst plots each car's age in years on the x-axis against its resale value in dollars on the y-axis. Older cars generally sell for less, and the points fall close to a single downward straight-line path. One 12-year-old car breaks the pattern: it sits well above the line, selling for far more than its age predicts because it is a sought-after collector model. Identify the explanatory and response variables and give a four-part description of the association.

  1. Identify the variables. Age is used to predict value, so age is the explanatory variable (x-axis) and resale value is the response variable (y-axis).

  2. Form. The points follow a straight-line path, so the form is linear.

  3. Direction. As age increases, value tends to decrease, so the direction is negative.

  4. Strength. The points fall close to the line, so the association is strong.

  5. Unusual features. The 12-year-old collector car sits far above the straight-line path, selling for much more than its age predicts, so it is a point that does not fit the general trend.

Age is explanatory and resale value is the response. The association is linear, negative, and strong, with one unusual point: a 12-year-old collector car that sells for far more than its age predicts. In context: older sedans tend to have lower resale values, and the tight pattern means age predicts value well for the rest of these cars.

Frequently asked questions

How do I decide which variable is explanatory and which is the response?

Ask which variable you are using to predict or explain the other. The predictor is the explanatory variable and goes on the x-axis, while the variable being predicted is the response and goes on the y-axis. If neither clearly predicts the other, the roles are a judgment call set by the context of the question.

Does a scatterplot need both variables to be quantitative?

Yes. A scatterplot in topic 5.1 shows two quantitative variables, meaning both are numerical measurements taken on the same individuals. A relationship that involves a categorical variable is displayed and summarized with different tools.