Solving Data Inference & Margin of Error Questions on the SAT
These Digital SAT questions give you a sample statistic — a percentage, a count, or a margin of error — and ask you to scale it to the full population or read the range of plausible values correctly.
Problem-Solving and Data Analysis · Updated October 21, 2026 · 10 min read
01
The method: Sample → Scale → Interval
A well-chosen random sample lets you estimate a fact about an entire population without surveying everyone. The core move is always the same: find the sample's proportion, then multiply that proportion by the population size. If a margin of error is given, apply it to the proportion (or count) before or after scaling — just stay consistent.
Use Sample → Scale → Interval. First, find the sample proportion (part ÷ sample size). Second, scale it up by multiplying by the total population. Third, if a margin of error is given, apply it as ± to get a range instead of a single number.
A random sample of 250 students from a school of 2,000 found that 150 plan to attend college out of state, with a reported margin of error of 4 percentage points. Walk through scaling both the estimate and its interval below.
Scale a sample to a population
Step 1 · Proportion
150 / 250 = 0.60
60% of the sample plans to attend college out of state.
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A random sample of 400 voters in a city of 50,000 found that 220 support a ballot measure. Based on this sample, about how many of the 50,000 voters support the measure?
02
Scaling a sample proportion to the population
Scaling only works if the sample is genuinely random and representative of the population you're trying to describe. The arithmetic — proportion times population — is simple; the SAT usually tests whether you set it up correctly (using the right population size, not the sample size) more than whether you can multiply.
Watch for the two numbers being easy to swap: the sample size is the denominator when you find the proportion, and the population size is what you multiply that proportion by afterward.
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A random sample of 120 of the 3,600 items in a shipment found 9 defective. Estimate the total number of defective items in the shipment.
Lock this skill with free SAT Math practice.
Sample-to-population questions appear throughout Problem-Solving and Data Analysis. Drill today's free Math set — no account required.
A margin of error turns a single point estimate into a range of plausible values: estimate − margin to estimate + margin. It's applied symmetrically — the same amount is added and subtracted. As a rule of thumb, larger sample sizes tend to produce smaller margins of error, since more data narrows the range of uncertainty.
Read the interval correctly
1 / 3
Pick the correct interval or outcome for each scenario.
A poll estimates 42% support, with a margin of error of 3%. What's the interval?
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A survey estimates that 34% of residents favor a proposal, with a margin of error of 5 percentage points. Which of the following is NOT a plausible value for the true percentage of residents who favor the proposal?
04
What you can (and can't) conclude
A margin of error only accounts for random sampling variability — the fact that different random samples give slightly different results by chance. It does not fix other problems, like a biased sample, poorly worded questions, or nonresponse. A wide margin of error doesn't make a biased survey trustworthy.
Just as important: a sample's results only generalize to the population it was actually drawn from. A random sample of adults in one city tells you about that city's adults — not about children, not about a different city, and not automatically about the whole country.
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A survey of 500 randomly selected adults in City A found that 62% support a new transit line. Which conclusion is best supported by this survey?
05
Practice until it's automatic
These mix scaling a sample to a population, building and reading margin-of-error intervals, and judging what a sample does and doesn't support.
A random sample of 80 out of 4,000 parts finds 6 defective. Estimate the total defective parts.
A poll estimates 55% support, with a margin of error of 4%. Give the interval.
An estimate is 900 people, with a margin of error of 60 people. Give the interval.
True or false: a margin of error accounts for bias caused by poorly worded questions.
A random sample of 50 out of 1,000 books finds 8 damaged. Estimate the total damaged books.
If a sample size increases while the sampling method stays the same, the margin of error typically...
Once scaling and intervals feel automatic, the next question is whether a sample supports a stronger claim — like cause and effect — which is exactly what evaluating statistical claims is about.
06
Practice questions
Here are three Inference and Margin of Error questions from our problem sets, from easier to harder, in the same format as the Digital SAT. Answer each one to see the full explanation.
Question 1 · Easy
A librarian selected 60 books at random from the 1,800 books in a library's collection and found that 9 of the selected books need repair. Based on this sample, what is the best estimate of the number of books in the collection that need repair?
Question 2 · Medium
A forester selected 250 trees at random from the 12,000 trees in a state forest and found that 18% of the selected trees showed signs of blight. The margin of error for the estimate is 4 percentage points. Based on these results, which of the following is a plausible number of trees in the forest that show signs of blight?
Question 3 · Hard
A researcher selected 500 students at random from the 4,200 students at Westbrook High School and found that 32% of the selected students walk to school. The margin of error for the estimate is 4 percentage points. Which of the following claims about the students at Westbrook High School are supported by these results? I. More than 1,100 students walk to school. II. Fewer than 1,400 students walk to school. III. At least one-fourth of the students walk to school.
There are 5 Inference and Margin of Error problem sets. Each set has around ten questions like these, with a full explanation for every answer.
A random sample of 300 of the 9,000 residents in a town found that 210 recycle regularly. Based on this sample, about how many of the 9,000 residents recycle regularly?
Practice 2
A poll estimates that 47% of voters support a candidate, with a margin of error of 4 percentage points. Which value is NOT within the plausible range for the true percentage?
Practice 3
A study estimates that 1,500 ± 120 users prefer a new app design. What is the range of the estimate?
Practice 4
A random sample of 400 employees at Company X found that 65% prefer remote work. Which conclusion is valid?
Practice 5
Two surveys ask the same question the same way. Survey 1 samples 100 people; Survey 2 samples 1,000 people. Which survey is likely to have the smaller margin of error?
07
Frequently asked questions
What is margin of error on the SAT?
A margin of error turns an estimate from a random sample into a range of plausible values for the whole population: the estimate minus the margin up to the estimate plus the margin. College Board's framework says SAT questions on this skill ask you to interpret margin of error and to understand that a larger sample size generally leads to a smaller margin of error. If a sample estimates 40% with a margin of error of 3 percentage points, any value from 37% to 43% is plausible for the population.
How do you estimate a population total from a sample?
Find the sample proportion (the part divided by the sample size), then multiply it by the size of the whole population. If 12 of 80 randomly chosen light bulbs are defective, the proportion is 0.15, so about 0.15 × 2,000 = 300 of 2,000 bulbs are defective. The usual slip is multiplying by the sample size instead of the population size.
Does a larger sample always give a smaller margin of error?
Generally, yes, and that is how College Board words it: a larger sample size generally leads to a smaller margin of error. The comparison assumes both samples are chosen the same random way. A bigger sample does nothing to fix a biased method, such as surveying only people who volunteer to answer.
What does a margin of error not tell you?
It doesn't tell you the true population value, only a range where that value plausibly falls. It covers chance variation between random samples, not bias from a self-selected sample, a leading question or people who didn't respond. And it applies only to the population the sample was drawn from, so a margin of error from one school says nothing about another school.
How hard are SAT margin of error questions?
In our experience the arithmetic is light and reading the interval correctly is the hard part. College Board's Skills Insight lists selecting plausible values of a population mean or proportion, given a sample mean or proportion and its margin of error, among the skills students in the 550–600 Math score band typically show.
How many SAT questions are about sampling and margin of error?
College Board doesn't publish a count for this skill alone. It is one of seven skills in Problem-Solving and Data Analysis, which makes up about 15% of the scored Math questions, or 5 to 7 questions, shared across all seven skills.
Next up
Keep going in SAT Math.
Evaluating statistical claims builds directly on sample-to-population reasoning.