Represent two-variable quantitative data with scatterplots and describe the association by its form, direction, strength, and any outliers (A.DSR, Data and Statistical Reasoning).

What this topic is asking

This Data and Statistical Reasoning (A.DSR) standard moves from one variable to two, asking you to build and read a scatterplot and to describe the association between two quantitative variables. The Georgia Milestones EOC tests this as the entry point to bivariate data: you describe a relationship by its form (linear or not), direction (positive or negative), strength (how tightly the points cluster), and any outliers or clusters. It is the visual groundwork for fitting a line and interpreting correlation, the next two topics.

Building and reading a scatterplot

A scatterplot plots each data pair $(x, y)$ as a single point, with the explanatory variable on the horizontal axis and the response variable on the vertical axis. It reveals whether two variables move together and how.

The four features of an association

A complete description of a scatterplot names four things.

• Form: is the pattern linear (points follow a straight line) or nonlinear (curved)?
• Direction: positive if $y$ tends to increase as $x$ increases; negative if $y$ tends to decrease as $x$ increases.
• Strength: strong if the points cluster tightly around a line or curve; weak if they are loosely scattered.
• Outliers and clusters: individual points that fall far from the pattern, or distinct groups of points.

How the Milestones examines this topic

• Multiple choice. Describe the direction and strength of a shown scatterplot.
• Hot spot. Identify an outlier or a cluster on a scatterplot.
• Constructed response. Give a full description (form, direction, strength, outliers) of a relationship.

Why all four features matter

Each feature answers a different question, and the EOC rewards naming them separately rather than blurring them. Form tells you whether a straight-line model is even appropriate: if the points curve, a line will fit poorly no matter how tight the band, and you would need a different model. Direction tells you the practical meaning, whether more of $x$ comes with more or less of $y$ (more studying with higher scores is positive and sensible). Strength tells you how trustworthy a prediction from the trend would be: a tight band supports confident predictions, a loose cloud does not. Outliers flag points that may be errors or special cases and that can distort a fitted line. Because each feature carries distinct information, a one-word answer like "positive" is incomplete; the full four-part description is what a constructed-response rubric expects, and it sets up the line-of-best-fit work that follows.

Distinguishing no association

A frequent EOC distractor is "no association." A scatterplot shows no association when the points form a shapeless cloud with no upward or downward trend, so knowing $x$ tells you nothing about $y$. This is different from a weak association, which still has a faint trend. Recognizing a true no-association cloud (random scatter) versus a weak but real trend is a judgment the EOC tests, and it matters because fitting a line to data with no association produces a near-flat, meaningless model.

Try this

Q1. A scatterplot of temperature versus hot-chocolate sales shows points falling as temperature rises, loosely scattered. Describe direction and strength. [1 point]

• Cue. Negative direction, weak strength.

Q2. Points form a curved (U-shaped) pattern. Is the form linear or nonlinear? [1 point]

• Cue. Nonlinear (a line would not fit the curve).