Solving Data Inference & Margin of Error Questions on the SAT

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.

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.

Margin of error: reading the interval

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.

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.

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.

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.

Practice questions

Here are five practice problems that help you hone your skills. Use the same method we learned earlier above to solve these problems. Remember, practice makes perfect.