SAT Math — percentages, spread and what a sample proves

Thirteen questions across the whole domain — ratios and rates, percentages, one- and two-variable data, probability from a two-way table, and inference from a sample. The arithmetic in almost all of them is easy. The difficulty is reading precisely, and the questions are built around the specific places where reading loosely gives you a wrong answer that feels right.

Percent against percentage points. A rate that goes from 5% to 7% has risen by two percentage points and by forty percent, and those are different sentences describing the same event. A question asking "by what percent did it increase" has one answer, and the other number is sitting among the options. Both of the other wrong choices here are real arithmetic errors: dividing the change by the finishing value instead of the starting one, and giving the ratio of new to old rather than the increase.

Mean against median. An outlier drags the mean and leaves the median more or less where it was. Removing a low score raises the mean of what is left. Neither of these needs a calculation, and both appear as questions.

A line of best fit is a prediction. Its slope is the predicted change per unit, its intercept the prediction at zero, and neither is a promise about any individual.

Conditional probability. "Of the people who exercise regularly, what fraction sleep well" has a denominator of the regular exercisers, not of everybody. Deciding what the denominator is before computing anything is the whole question.

What a study lets you say. The most tested idea in the statistics part of the SAT, in two halves, and both are here:

• Random selection lets you generalize — but only to the population you selected from. A random sample of people leaving one train station tells you about people leaving that train station, and not about every adult in the city.
• Random assignment is what licenses a causal claim. An observational study, however large and however clean, shows an association. The wrong answers overreach in exactly these two directions, every time.

And a third failure worth naming: a mean is not a statement about any individual. A mean commute of 47 minutes is entirely consistent with commutes of 10 minutes and 90 minutes.

Margin of error in one sentence: it is the range in which the true population value plausibly sits, and it shrinks as the sample grows.

The twelve flashcards carry the rules as sentences you can recite, which is what these questions actually reward — this domain is only 5 to 7 questions on the real test, and most of them are won or lost on a definition.

• Compute a percent change against the starting value, and tell it apart from a change in percentage points
• Predict what happens to the mean and to the median when an outlier is added or removed
• Interpret the slope and intercept of a line of best fit in context
• Decide the correct denominator before computing a conditional probability
• Generalize a random sample only to the population it was actually drawn from
• Refuse a causal claim from an observational study, however large
• Read a mean as a property of the group and not of any individual in it
• State what a margin of error does and does not tell you
• Convert between rates and totals with the units under control

Written for this catalog, with no source document. The content follows the skills named in the College Board's public description of the SAT Problem-Solving and Data Analysis domain (satsuite.collegeboard.org, checked 2026); every question, option and explanation here is original. Zestly is an independent study tool. It is not affiliated with the College Board, which owns the SAT.