SAT Problem-Solving and Data Analysis: Real-World Math, Careful Setup

This domain is less about advanced formulas and more about careful setup, reading a word problem, a table, or a scatterplot correctly and translating it into the right calculation. The math itself is usually simple; the questions are designed to catch a rushed setup.

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Did you know

Problem-Solving and Data Analysis makes up roughly 15% of the Math section, tied with Geometry and Trigonometry for the smallest math domain, but its questions tend to be more about reading carefully than heavy calculation, which makes them some of the fastest points available if you don't rush the setup.

What's tested

Ratios, rates, proportions, and units

Scale a recipe, convert units, or set up a proportion correctly.

Learn more: setting up a proportion without flipping it

Keep the same units in the same position on both sides of a proportion, "miles over hours" on the left has to be "miles over hours" on the right, not "hours over miles." Mixing this up is the single most common error here.
Cross-multiply once you've set it up correctly rather than trying to solve fractions in your head, it's more reliable under time pressure.
For unit conversion chains (like converting a speed from miles per hour to feet per second), write out each conversion factor as a fraction so the units you don't want visibly cancel.

Percentages

Percent increase, percent decrease, and percent-of comparisons.

Learn more: percent change versus percent of

Percent change is always (new − original) / original, not new divided by original. Mixing these up is a very common, very avoidable error.
"20% more than x" means 1.2x, and "20% less than x" means 0.8x. Converting a percent change directly into a multiplier is faster than calculating the percentage and adding or subtracting it as a separate step.
For back-to-back percent changes (a price goes up 10%, then down 10%), don't assume they cancel out. Multiply the factors in sequence (1.1 × 0.9), the answer is not the original value.

One-variable data: statistics

Mean, median, mode, standard deviation, and how outliers or shifting the whole data set affects them.

Learn more: how a shift or an outlier changes each statistic

Adding the same number to every value in a data set shifts the mean and median by that same amount, but does not change the standard deviation, spread is unaffected by a uniform shift.
Multiplying every value by the same number multiplies the mean, median, and standard deviation all by that factor.
An outlier pulls the mean toward it but barely moves the median. Questions comparing mean and median after adding an extreme value are testing exactly this.
You won't usually need to calculate standard deviation by hand, questions typically ask you to compare which of two data sets has a larger or smaller spread, which you can often answer just by eyeballing how clustered the values are.

Two-variable data: models and scatterplots

Read a scatterplot, pick the line or curve of best fit, and interpret what a slope or the correlation means.

Learn more: matching a trend to the right kind of model

If the points roughly form a straight line, it's a linear model. If they curve consistently upward with increasing steepness, that's often exponential, not linear, don't force a straight-line answer onto a curved pattern.
The slope of a line of best fit represents a rate in context, "increase per year," "dollars per unit." Read the axis labels to know what that rate actually means before answering.
A point's residual is how far it sits from the line of best fit. A question asking which data point is "least accurately predicted by the model" is asking for the point farthest from the line, not the highest or lowest point.

Probability and inference

Basic and conditional probability from a table, plus questions about sample statistics and margin of error.

Learn more: reading a two-way table correctly

Basic probability is just favorable outcomes over total outcomes, the hard part is usually finding the right numbers in a two-way table, not the division itself.
Conditional probability ("given that...") shrinks your denominator. Once you're told a condition is true, only consider the row or column that matches it, don't use the whole table's total anymore.
A larger, more random sample gives a smaller margin of error. Questions about improving a survey's reliability are almost always testing this one idea.

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Gotcha

A classic trap: "a shirt's price increases by 20%, then decreases by 20%. Is the final price the same as the original?" It's tempting to think the two percentages cancel out, but they don't, the second 20% is taken off a larger number than the first 20% was added to. The final price is always slightly lower than the original. Whenever you see two percent changes applied in sequence, multiply the factors together instead of assuming they cancel.

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Quick tip

Before doing any calculation, restate what the question is actually asking for in plain words, "the new total after the discount," not "20% of 80." A surprising number of wrong answers come from correctly calculating the wrong thing.

Reading about the traps is step one.

Ember has original Problem-Solving and Data Analysis questions, each with the reasoning explained the same way, including exactly which trap answer it's testing.

Practice Problem-Solving and Data Analysis now