Question 24·Hard·Command of Evidence
Correlations Between Congestion Ratings and Features of the Crowd in Raters’ Immediate Vicinity
| Crowd feature | Before obstacle | After obstacle | Overall |
|---|---|---|---|
| Density | |||
| Velocity |
Researcher Xiaolu Jia and colleagues monitored individuals’ velocity and the surrounding crowd density as a group of study participants walked through a space and navigated around an obstacle. Participants rated how congested it seemed before the obstacle, after the obstacle, and overall, and the researchers correlated those ratings with velocity and density. (Correlations range from to , with greater distance from indicating greater strength.) The researchers concluded that the correlations with velocity are stronger than those with density.
Which choice best describes data from the table that support the researchers’ conclusion?
For SAT chart-and-table evidence questions, first underline the key claim you need to support (here, that correlations with velocity are stronger than those with density). Then quickly recall or note how the relevant measure works (correlation strength = distance from ). Compare the numbers in an organized way—row by row or category by category—and look for a consistent pattern. Finally, choose the answer that clearly and directly summarizes that pattern using the right comparison; avoid choices that are numerically true but compare the wrong quantities or focus on irrelevant details (like sign instead of strength).
Hints
Focus on what needs to be supported
Reread the sentence with the researchers’ conclusion. What specific comparison are they making between correlations with velocity and correlations with density?
Use the definition of strength of correlation
The passage tells you how to judge correlation strength: it depends on how far the value is from , not on whether it is positive or negative. For each rating, compare how far the velocity correlation and the density correlation are from .
Look for a choice that summarizes a pattern across all three ratings
After you compare density vs. velocity for “before obstacle,” “after obstacle,” and “overall,” think about what general statement describes all three comparisons, and then see which option matches that statement.
Step-by-step Explanation
Understand what the researchers concluded
The researchers concluded that correlations with velocity are stronger than correlations with density. The passage also reminds you that correlations range from to , and a correlation is stronger the farther it is from , regardless of whether it is positive or negative. So you must look for an answer choice that compares the strength (distance from ), not just the sign.
Compare one pair of correlations using distance from 0
Start with the “Before obstacle” rating:
- Density correlation:
- Velocity correlation:
To compare strength, compare their distances from :
Since , the correlation with velocity is stronger than the correlation with density for the “before obstacle” rating.
Check the same comparison for the other ratings
Repeat the comparison for the “After obstacle” and “Overall” ratings:
-
After obstacle:
- Density: → distance from is
- Velocity: → distance from is (stronger)
-
Overall:
- Density: → distance from is
- Velocity: → distance from is (stronger)
In both cases, the velocity correlation is again stronger than the density correlation. Now you need the choice that accurately summarizes this pattern and directly supports the researchers’ conclusion.
Match the correct summary to the data and conclusion
You are looking for a statement that says, in effect, that for each rating (before, after, overall), the correlation with velocity is stronger than the corresponding correlation with density, using the idea of being farther from .
The statement “For each of the three ratings, correlations with velocity are further from than the corresponding correlations with density are.” matches all three comparisons, so it supports the researchers’ conclusion and is the correct answer.