A Checklist for a Complete Scatterplot Description
In “Identifying Clusters and Gaps,” you learned to look for groups and empty regions as well as individual points. Now bring that skill together with the earlier descriptions of direction, form, strength, and outliers. A useful checklist for describing one scatterplot is DUFS: direction, unusual features, form, and strength.
DUFS is a checklist, not a calculation or a statistical procedure. It helps you make sure a description addresses the key visible features, then combine those observations into a readable paragraph. You do not need to force a category when the graph does not support one: for example, a scatterplot may have no clearly unusual points, or no single overall direction.
The order is practical. First describe how \(y\) tends to change as \(x\) increases. Next check for observations or regions that stand out from the rest. Then identify the pattern’s shape. Finally, judge how closely the points follow that shape. You may notice these features in a different order while looking at a graph, but a finished description should make each one clear.
Moving from left to right, does \(y\) generally increase, decrease, or show no clear overall increase or decrease?
Look for outliers, clusters, gaps, or other departures from the main pattern. If none stand out, say so when it helps make the description complete.
Is the overall pattern roughly straight (linear), curved (nonlinear), or better described in another way, such as separate clusters?
How closely do the points follow the overall pattern? Describe the association as strong, moderate, or weak when those words fit the display.
The topics in this checklist build on earlier tutorials. “Describing Direction in a Scatterplot” explains positive and negative direction; “Recognizing Linear and Nonlinear Form” covers shape; “Judging Strength of an Association” focuses on how closely points follow a pattern; and “Spotting Outliers in Bivariate Data” and “Identifying Clusters and Gaps” cover unusual features. DUFS brings these parts into one description rather than replacing those ideas.
Describe the Pattern and Its Exceptions Separately
A useful description distinguishes the overall pattern from anything that does not fit it. For instance, a scatterplot can show a positive, roughly linear association for most points and also have one point far above that pattern. Calling the entire graph “positive and strong” without mentioning the point leaves out important information. On the other hand, an unusual point does not automatically erase the overall pattern.
“Unusual features” is a broad checklist item. It can include a bivariate outlier, a cluster, a gap, or a noticeable change in the pattern. Use the more specific term when the graph supports it. As discussed in “Identifying Clusters and Gaps,” a cluster is a concentration of observations and a gap is a sparse or empty region; neither should be confused with one point far from the pattern.
Form and strength go together. Judge how closely points follow the shape you see, whether that shape is straight or curved. A strong curved association can be strong even though it is not linear. Do not call a curved pattern weak just because a straight line would not describe it well. Likewise, a linear pattern can be weak if points are widely scattered around its general direction.
Worked Example: Charging Time and Battery Level
A fictional technician records charging time, \(x\), in minutes, and battery level, \(y\), as a percentage for nine devices under the same demonstration setup. The values below are invented. Consider the scatterplot of these paired observations.
| Device | Charging time, \(x\) (minutes) | Battery level, \(y\) (percent) |
|---|---|---|
| A | 10 | 18 |
| B | 20 | 25 |
| C | 30 | 32 |
| D | 40 | 39 |
| E | 50 | 47 |
| F | 60 | 53 |
| G | 70 | 62 |
| H | 80 | 68 |
| I | 90 | 96 |
Direction. Most of the points rise from left to right: devices with longer charging times generally have higher battery levels. The direction is positive.
Unusual features. Device I, at 90 minutes and 96%, lies well above the increasing pattern formed by the other devices. It is a possible bivariate outlier because it stands apart from that pattern, not merely because it has a large \(x\)- or \(y\)-value.
Form and strength. The first eight points follow a roughly straight, positive pattern fairly closely. The separated point changes how closely all nine points follow that pattern, so the description should mention it rather than assigning a strength label as though it were absent.
Complete DUFS description. “Battery level tends to increase as charging time increases, showing a positive, roughly linear association for most devices. The first eight points follow this pattern fairly closely, but the device recorded at 90 minutes and 96% lies well above it and is a possible bivariate outlier. The strength of the overall pattern is affected by this unusual point.”
That description reports the visible association without claiming that charging time alone caused the battery levels or that the unusual point is an error. The plot can prompt a data check, but it does not establish why that observation is different.
Direction Can Change in a Nonlinear Pattern
The direction of a nonlinear pattern may not be summarized by one word for the entire graph. If \(y\) decreases as \(x\) increases over one part of the display and increases over another, say so. Writing only “positive” or “negative” could hide the shape that makes the pattern meaningful.
For a curved association, judge strength by how closely the points follow the curve. This is an important use of the DUFS checklist: it prevents “linear” from being treated as another word for “strong.” A scatterplot can have a clear, strong association with a distinctly nonlinear form.
Worked Example: Outdoor Temperature and Building Energy Use
A fictional facilities team records outdoor temperature, \(x\), in degrees Celsius, and a building’s daily energy use, \(y\), in hundreds of kilowatt-hours, on eight days. The invented observations are listed here.
| Day | Temperature, \(x\) (°C) | Energy use, \(y\) (hundreds of kWh) |
|---|---|---|
| A | 8 | 92 |
| B | 12 | 75 |
| C | 16 | 59 |
| D | 20 | 46 |
| E | 24 | 40 |
| F | 28 | 47 |
| G | 32 | 64 |
| H | 36 | 87 |
Direction. Energy use first tends to decrease as temperature increases, reaching its lowest values near the middle of the observed temperatures. At higher temperatures, energy use tends to increase. There is no single positive or negative direction across the full range.
Unusual features. The observations form one broad curved pattern. No individual point clearly stands apart from it, and there is no obvious separate cluster or gap.
Form and strength. The pattern is clearly curved rather than roughly straight. The points lie fairly close to that curve, so the nonlinear association appears strong.
Complete DUFS description. “Energy use decreases as outdoor temperature increases over the lower part of the range, then increases over the higher part, forming a strong, roughly U-shaped nonlinear association. No individual point, cluster, or gap clearly stands out from the overall curve.”
The description does not claim that temperature causes the energy-use pattern. Other features of the building or the days observed could matter, and the scatterplot alone cannot identify a cause.
Use the Checklist Even When a Feature Is Not Obvious
A complete description does not require every graph to have an obvious outlier, a dramatic curve, or an unmistakably strong association. Sometimes points form a diffuse cloud with no clear direction or shape. In that case, say that no clear association is visible rather than inventing a pattern. If a feature is uncertain, use careful wording such as “there appears to be” or “the pattern is roughly.”
The labels strong, moderate, and weak are qualitative descriptions of the scatterplot. They do not have universal numerical cutoffs. Compare the points with the pattern they seem to follow, and choose a word that matches the visible amount of scatter. “Judging Strength of an Association” develops that judgment; for now, the essential point is to describe strength in relation to form.
Worked Example: Commute Distance and Travel Time
A fictional transportation class records commute distance, \(x\), in kilometers, and travel time, \(y\), in minutes, for eight invented trips. The scatterplot shows one group of trips from a nearby route and another group from a longer route; the route labels are known.
| Trip | Route label | Distance, \(x\) (km) | Travel time, \(y\) (minutes) |
|---|---|---|---|
| A | Nearby | 2 | 12 |
| B | Nearby | 3 | 16 |
| C | Nearby | 4 | 15 |
| D | Nearby | 5 | 20 |
| E | Longer | 14 | 31 |
| F | Longer | 15 | 36 |
| G | Longer | 16 | 34 |
| H | Longer | 17 | 40 |
Direction. Across the displayed points, longer distances generally go with longer travel times, so the overall direction is positive.
Unusual features. The points form two clusters associated with the route labels. The nearby-route trips have distances from 2 to 5 km and travel times from 12 to 20 minutes; the longer-route trips have distances from 14 to 17 km and times from 31 to 40 minutes. There is a gap between the clusters in both variables. This uses the distinctions from “Identifying Clusters and Gaps.”
Form and strength. Within each cluster, the points show a roughly positive, nearly linear pattern. Describing the full display as one simple linear cloud would hide the groups. The points within each cluster follow their local patterns fairly closely, but the two separated clusters are an important part of the overall form.
Complete DUFS description. “Across the observed trips, distance and travel time have a positive association. The scatterplot contains two clusters, corresponding to the nearby and longer routes, with a gap between them in both distance and travel time. Within each cluster, the association is roughly linear and fairly strong; the full display is better described as two clusters than as one undifferentiated linear pattern.”
The route labels help describe which observations belong to each cluster, but they do not show why the routes differ or prove that distance alone explains travel time. A careful description reports the pattern and its limits.
Common Mistakes and AP Exam Tips
- Leaving out one of the four parts: A response that gives direction and strength but omits a visible curve or outlier is incomplete. Use DUFS to check your final description.
- Calling every association linear: A positive or negative direction does not guarantee a straight pattern. Inspect the form, including possible bends or separate clusters.
- Calling a nonlinear pattern weak because it is curved: Strength concerns how closely the points follow the pattern, not whether the pattern is straight.
- Letting an outlier disappear into a summary: Describe the main pattern and then state how the unusual point differs from it. Do not silently ignore a point that stands out.
- Using vague descriptions: “The graph goes up” is less complete than saying which variable tends to increase as the other increases, and identifying form and strength.
- Claiming a cause: An association in a scatterplot does not, by itself, prove that changes in \(x\) cause changes in \(y\). Describe the pattern, not an unsupported explanation.
- Forcing a strength or direction label: If the pattern is not clear, say so. A careful “no clear overall direction” is better than an inaccurate positive or negative label.
For full credit, write in context and make each part specific to the graph. State how the response tends to change as the explanatory variable increases, identify notable features or say none are apparent, describe the form, and characterize how closely the points follow it. If there are separate groups, bends, or outliers, include them rather than pretending the scatterplot has only one simple pattern.
Check Your Understanding
Use the DUFS checklist to plan a description of each scatterplot. Explain what you would mention and why.
- A scatterplot rises from left to right in a roughly straight pattern, but one point lies far below the others. What should your description say about direction, unusual features, form, and strength?
- A scatterplot follows a close, U-shaped curve. Why is “weak linear association” not an accurate complete description?
- A display has two labeled clusters, each with a positive trend, and a gap between them. Which features belong in a DUFS description?
- A scatterplot looks like a diffuse cloud, with no obvious overall direction or shape. What is a careful way to describe direction and form?
- Why should a description of a positive association avoid claiming that increasing \(x\) caused \(y\) to increase?