Build the concept, interpret evidence, and apply it in a separate assessment pool.
Learn: Evidence and decisions
Read each point in the correct order
A point records one paired observation. Locate its horizontal coordinate first, then read the corresponding vertical coordinate. Check the axis labels, scale, and units before comparing points.
Describe the overall pattern
Use the full cloud of points to describe positive, negative, or little apparent association. A straight-line pattern may support a constant rate; scattered data may not.
Interpret carefully
A visible association describes how two variables move together in the observed data. It does not, by itself, show that one variable caused the other.
Bubble charts encode a third variable
Read the horizontal and vertical coordinates as in a scatterplot. Then read the size key: in this lesson, bubble area represents employee count. A bubble with twice the radius has four times the area. Compare ratios such as revenue per employee using the stated values; the highest point need not have the greatest profit.
Use actual plotted coordinates
For each observation, pair its numerical x-value with its y-value. Calculate a rate between the two points named in the question; do not assume that unplotted points lie on a straight segment unless the question supplies that model.
Compare rates over matching intervals
For an interval from x=a to x=b, use (y_b−y_a)/(b−a). A larger vertical change alone does not imply a larger rate when the horizontal intervals differ.
Learning Objectives
Read ordered pairs from horizontal and vertical axes.
Describe direction and linear pattern from the full set of points.
Calculate a rate of change when the plotted relationship is linear.
Separate association in the data from a causal explanation.
Interpret a third variable encoded by bubble area.
Combine coordinates and bubble quantities to compare profit and per-person measures.
Use the requested answer precision to decide whether a comparison needs a value, direction, rate, or supported inference.
Prerequisite Knowledge
Coordinate pairs: the first value is the horizontal input and the second is the vertical response.
Slope as change in response divided by change in input.
Worked Examples
A negative association can contain local increases
Each point represents a different machine. Compare the overall pattern with the stronger claim that every older machine produces fewer units.
Machine age and weekly output■ Machines┄ Least-squares trend
Read the axis labels, scale and units before comparing values.
Read the cloud of observations: output generally falls as age increases. An overall association does not require every consecutive pair to decrease.
Test the word every with a counterexample. The 3-year-old machine produces more than the 2-year-old machine.88>86
Do not treat the observations as a controlled experiment. Age may be associated with maintenance, machine design, or usage.
Conclusion: The graph supports a negative overall association, contradicts a strictly decreasing pattern across every observed age, and does not establish causation.
Read a scattered positive trend
Ten observations are plotted at inputs 1 through 10. The responses vary around an increasing trend rather than lying exactly on one line.
Measured response versus input■ Measured┄ Least-squares trend
Read the axis labels, scale and units before comparing values.
Compare the endpoints to estimate the average change across the full observed range.(1,2),(10,17),mavg=10−117−2=35
Notice that local changes vary: for example, response rises from 2 to 5, then falls from 5 to 4. The dashed least-squares line summarizes the overall association; it does not pass through every point.
The plot is observational, so an upward association does not establish causation.
Conclusion: The data show a positive but scattered association. The average endpoint rate is 5/3 response units per input unit; individual intervals do not share one constant rate.
Read three variables in a bubble chart
Branches differ in revenue, operating margin and employee count. Find the branch with greatest profit and compare staffing at A and B.
Read horizontal and vertical positions separately. Profit is revenue multiplied by the margin.PA=2(0.10)=0.2,PB=4(0.20)=0.8,PC=6(0.15)=0.9,PD=8(0.25)=2
Use the area key for staffing. B has four times A’s employees. Its radius is only twice as large.2080=4,rArB=4=2
Conclusion: D has the greatest profit. B has four times the employees of A. Position, area and radius encode different things.
Rate depends on both coordinate changes
Observed points are (2,5), (4,7), (7,13), and (10,16). Compare the average response rate from x=4 to x=10 with the rate from x=4 to x=7.
Use the named endpoints for each interval.r4,10=10−416−7=1.5,r4,7=7−413−7=2
The first response change is larger, but its input interval is twice as long.
Conclusion: The average rate is 1.5 response units per input unit from 4 to 10, compared with 2 from 4 to 7.
Describe association without claiming causation
The measured values generally decrease as the input increases, but the graph is observational.
Describe the pattern across the plotted points.
Check whether the graph includes an experimental design or other causal evidence. A scatterplot alone does not.
Conclusion: The data show a negative association. They do not establish that changing the input causes the response to fall.
Think Like a GMAT Test-Taker
Read both axis labels and units before reading coordinates.
Use points that are far apart on a straight trend to compute slope, then check another interval.
Describe the pattern as observed; do not infer a cause that is not in the evidence.
For each bubble, record the three quantities before calculating. Check whether the size key describes area or radius.
Read both completion statements first, then inspect the axis labels, scale, units and answer choices to identify the required operation.
Separate observed points from a fitted trend; use only plotted coordinates for exact-value questions.
Common Traps
Swapping the horizontal input and vertical response.
Using the highest point alone to describe the trend.
Treating correlation as proof of causation.
Doubling the radius doubles the count: false when area encodes count.