Sat · Math: Problem-Solving & Data Analysis
The Complete SAT Bible · Digital SATMath: Problem-Solving & Data Analysis
SAT Math: Problem-Solving & Data Analysis is the data-and-word-problem domain of the Digital SAT Math section. It is about 15% of the scored Math questions (roughly 5 to 7 of the 40), but it carries most of the word problems on the test, so the real skill is reading a situation and translating it. It spans the full arc from ratios, rates and proportions and percentages into one- and two-variable data and statistics, then probability, inference and margin of error, and evaluating statistical claims. Each skill is taught with charts and fully worked, step-by-step examples.
The Digital SAT presents these questions in two formats: multiple choice (four answer choices, A to D) and student-produced response (you type the answer directly; fractions or decimals are accepted, with no percent sign, dollar sign or commas). This guide teaches the method behind each question type, then drills it with 35 exam-difficulty questions across Easy, Medium and Hard, each worked in full with the trap behind every wrong choice. The domain is trap-dense: the wrong answer is usually a misread, not bad maths, so the winning move is to slow down on the set-up.
What SAT Math: Problem-Solving & Data Analysis covers
The whole domain → one exam-ready map. Nine parts, ratios and percentages through evaluating statistical claims, then 35 worked practice questions. Each links to its free chapter guide.
How the Digital SAT Math section assesses this
Only what this guide can support from the question set is stated below. Confirm current section structure, timing and tools on the official College Board test specifications before you rely on them.
| Item | Weight / count | What it means |
|---|---|---|
| Share of scored Math questions | ~15% | Problem-Solving & Data Analysis is about 15% of the scored Math questions, roughly 5 to 7 of the 40. It is also where most of the word problems live, with about 30% of all Math questions set in a real-world context. |
| Practice questions in this guide | 35 | This guide drills 35 exam-difficulty questions spanning all seven skills of the domain, each worked in full. |
| Multiple choice | 4 choices (A to D) | Each multiple-choice question gives four answer choices, A to D, with exactly one correct answer. |
| Student-produced response | Type the answer | You enter the answer directly. Fractions or decimals are accepted; no percent sign, dollar sign or commas. |
| Difficulty | Easy / Medium / Hard | Questions are tagged by difficulty across all topics, so you can build from confidence questions up to the hardest data and inference items. |
Split a total by a ratio
- Step 1Add the ratio parts to find the total number of parts. 3 + 5 = 8, so the $120 is divided into 8 equal parts.
- Step 2Find the value of one part by dividing the total by the number of parts. 120 ÷ 8 = 15, so each part is worth $15.
- Step 3Multiply each side of the ratio by the value of one part. The first share is 3 × 15 = $45; the second share is 5 × 15 = $75.
- Step 4Check that the shares add back to the total: 45 + 75 = 120. It matches, so the split is correct.
Key terms
- Unit rate
- A rate per one unit, such as miles per hour or dollars per item; you find it by dividing. A proportion is two equal ratios, solved by cross-multiplying.
- Percent change
- (new minus old) ÷ old × 100, always relative to the original value. To find a reverse percent (the original amount) you divide rather than multiply.
- Mean
- The arithmetic average, sum ÷ count. It is pulled toward outliers and skew, so in a right-skewed distribution the mean is greater than the median.
- Median
- The middle value of an ordered list. It resists outliers, which is why it can sit below the mean when the data are right-skewed.
- Interquartile range (IQR)
- Q3 minus Q1, the spread of the middle 50% of the data; it is read off the five-number summary shown by a box plot (min, Q1, median, Q3, max).
- Line of best fit
- The line that models a scatterplot's trend, used to predict y from x. Its slope is the rate of change and its y-intercept is the value at x = 0.
- Residual
- Actual minus predicted at a point: positive means the data point is above the line of best fit, negative means below it.
- Conditional probability
- P(A given B): the probability of A within the restricted universe of B. From a two-way table it is the count that is both A and B divided by the total in row or column B, not the grand total.
- Complement
- P(not A) = 1 minus P(A); a fast route to a probability when the unwanted outcome is easier to count.
- Margin of error
- The plus-or-minus half-width of a plausible interval for a population parameter: estimate plus or minus the margin of error. A larger sample size makes it smaller.
- Random selection vs assignment
- Random selection lets results generalize to the population. Random assignment to treatment and control lets a study claim causation; without it, an observational study shows only association, and a confounder may distort it.
SAT Math: Problem-Solving & Data Analysis FAQ
How much of SAT Math is Problem-Solving and Data Analysis?
It is about 15% of the scored Math questions, roughly 5 to 7 of the 40. It is also where most of the word problems live, with about 30% of all Math questions set in a real-world context, so careful reading matters more than memorised formulas.
How do I find a reverse percent, the original amount?
Divide, do not multiply. If 30 is 60% of a number, the number is 30 ÷ 0.60 = 50. Percent change is always taken over the original value: (new minus old) ÷ old.
When does an outlier change the mean more than the median?
Always. The mean is pulled toward an outlier or a skew, while the median resists. In a right-skewed distribution the mean is greater than the median; in a left-skewed one it is smaller.
How do I read a line of best fit on a scatterplot?
To predict, read the y-value on the line at a given x. To compare predicted with actual, the line gives the prediction and the data point gives the actual; their difference is the residual. The slope is the rate of change and the y-intercept is the value at x = 0.
How do I find a conditional probability from a two-way table?
Given that shrinks the universe. P(A given B) is the count that is both A and B divided by the total in that row or column B, not the grand total.
What does the margin of error tell me?
It is the plus-or-minus half-width of a plausible interval for the true population value: estimate plus or minus the margin of error. The parameter is plausibly, not certainly, inside it, and a larger sample size makes the margin of error smaller.
When can a study claim cause and effect?
Only with random assignment to treatment and control, which is an experiment. Random selection lets you generalize to the population. An observational study shows association, not causation, so watch for confounders.
Related SAT sections
Problem-Solving & Data Analysis is one of three SAT Math domains. Pair it with the other two, or step back to the full SAT overview.
How to study for SAT Math: Problem-Solving & Data Analysis
This domain is less about formulas and more about reading carefully, then not falling for the set-up traps. (1) Work it in three passes: learn the method from each worked example (for every chart, ask what a point, bar or interval means before reading on), drill the practice questions cold, then re-read the traps, because here the wrong answer is usually a misread rather than bad maths. (2) Slow down on the set-up: decide which value is the base of a percent, whether a ratio is part-to-part or part-to-whole, and which row or column is the restricted universe for a conditional probability. (3) Build a few reliable moves and reuse them: set up the ratio in parts, take percent change off the original (and divide for a reverse percent), restrict the universe before computing a conditional probability, and read residuals as actual minus predicted. (4) Master the term-vs-term distinctions the test rewards: mean vs median (and what skew does to each), random selection vs random assignment (generalize vs claim causation), and association vs causation. (5) Practise both formats: multiple choice (four choices) and student-produced response (type the answer; fractions or decimals, no percent sign, dollar sign or commas). (6) Confirm the current section structure, timing and on-screen tools on the official College Board specifications, since this guide states only what its question set supports.
