SAT / Math / Problem-Solving & Data Analysis / Data Analysis / Notes Math Problem-Solving & Data Analysis
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About 25 minutes On this page Essential concepts SAT strategy and application Mistakes and traps Key takeaways Data Analysis questions test careful reading as much as computation. Titles, axes, units, legends, scales, and comparison groups determine what a displayed value means and what conclusions are justified.
Essential concepts Bookmark Key concept A visual display is a measurement system Before using a value, identify its variable, unit, category, and time period. Nonzero axis baselines and unequal intervals can make visual differences look larger or smaller than they are.
Rule Distinguish percent change from percentage-point change A rate rising from 20% to 30% increases by 10 percentage points but by 50% relative to its original value.
Relative change \[ ext{relative change}=rac{ ext{new}- ext{old}}{ ext{old}}\]
Multiply by 100% when the question requests a percent change.
SAT strategy and application → SAT strategy and application Bookmark SAT strategy Write the comparison in words first State which two values must be compared and what operation the question requests. Then retrieve only those values from the display.
Find the change \(150-120=30\) thousand.
Divide by the original \(30/120=0.25\) .
Percent increase: 25%.
← Essential concepts Mistakes and traps → Mistakes and traps Bookmark Common mistake Ignoring units or scale A value labeled ‘150’ may mean 150 thousand, 150 million, or an index value. Carry the display’s units through the answer.
Common trap Inferring causation from a graph Two variables moving together establishes an association, not necessarily a causal relationship. Consider study design and alternative explanations.
Mini check Check your understanding A survey response rate rises from 40% to 46%. By how many percentage points did it rise?
6 15 40 46 Show answer and explanation Answer: 6 percentage points
Percentage-point change is the direct difference: 46 − 40 = 6.
← SAT strategy and application Key takeaways → Key takeaways What to remember Read titles, axes, units, legends, and scales before calculating. Identify the exact groups and values the question compares. Separate percentage points from relative percent change. Do not infer causation from association alone. ← Mistakes and traps Continue learning Put these notes into practice Apply the ideas with SAT-style questions, then reinforce key details with flashcards.