Census vs sample survey: all vs a random sample
By Jude Wallis · Published
A census collects data from every individual in the population, so it reports the parameter exactly. A sample survey collects data from only a randomly chosen subset and uses that sample to estimate the population, which is faster and cheaper but adds sampling variability.
AP Statistics: Unit 1 (topics 1.10, 1.11, 1.12). A census is defined in topic 1.10 of Unit 1 in the Fall 2026 AP Statistics course as recording information from all individuals in a population, and a survey as an observational study that collects data using a standard set of questions. Random sampling and its problems are topics 1.11 and 1.12. Unit 1 is 20% to 30% of the multiple-choice section.
Census vs sample survey: the short answer
Both are ways to gather data about a population, and the only structural difference is how many individuals you reach. A census records information from every item or individual in the population. A sample survey collects data from only part of the population, chosen with some random mechanism, and then uses that part to estimate the whole.
That difference in coverage drives everything else. A census, done perfectly, hands you the exact population value, called a parameter, with no guesswork. A sample survey hands you a statistic, a value computed from the sample, that stands in for the parameter you did not measure, so it comes with sampling variability: a different random sample would give a slightly different number.
What a census is
A census consists of recording information from all items or individuals in a population. If the population is the 1,200 students at one school, a census surveys all 1,200. Because you reach everyone, the summary you compute is the parameter itself, not an estimate of it.
The appeal of a census is certainty about the group you measured: there is no sampling error, because there is no sampling. The cost is practical. Reaching every individual can be expensive, slow, or impossible, and a large operation invites its own problems, such as people who do not respond or who are missed entirely. Those are nonsampling errors, and a census is not immune to them.
The US population count run every ten years is the textbook example of a census, and it shows both sides: full coverage in principle, but enormous cost and real trouble reaching everyone in practice.
What a sample survey is
A survey is an observational study in which data are collected from people using a standard set of questions. A sample survey applies those questions to a sample, a subset of the population selected by a random method such as a random number generator. You measure the sample, compute a statistic, and use it to estimate the population parameter.
The payoff is efficiency. A well-chosen random sample of a few hundred people can estimate a population of millions closely, at a tiny fraction of the cost of reaching everyone. The price you pay is uncertainty: because you did not measure the whole population, your estimate carries a margin of error that shrinks as the sample size grows.
The word random is doing real work here. A sample chosen at random lets you generalize to the population and lets you quantify how far off the estimate is likely to be. A sample chosen by convenience does neither, no matter how large it is. For the sampling schemes themselves, see simple random vs stratified sampling.
The differences side by side
| Feature | Census | Sample survey |
|---|---|---|
| Who is measured | Every individual in the population | A random subset of the population |
| What you get | A parameter (the exact value) | A statistic (an estimate) |
| Sampling error | None | Present, shrinks as the sample grows |
| Cost and time | High, sometimes prohibitive | Low relative to the population size |
| Margin of error | Not needed | Reported with the estimate |
| Main risk | Nonresponse, missed individuals | An unrepresentative or biased sample |
Every row traces back to coverage. A census measures all, so it needs no inference; a sample survey measures some, so inference is the whole point.
When to use which
Use a census when the population is small, reachable, and stable enough that measuring everyone is practical, or when you need the exact count rather than an estimate, such as a final class roster or a full inventory. Full coverage is worth the effort only when the effort is feasible.
Use a sample survey, which is the far more common choice, whenever a census would be too costly, too slow, or impossible, and an estimate with a known margin of error is good enough. That covers almost all polling, quality control, and research. A good sample survey often beats a sloppy census, because the resources saved by not chasing every individual can buy better questions, better follow-up, and less nonresponse. To plan the size of a sample, see the sample size calculator.
The classic mix-up and how to avoid it
The common error is treating a large sample as if it were a census, or treating a census as automatically more accurate than any sample. Sample size is not the same as coverage: a sample of 5,000 is still a sample, and it still yields a statistic with a margin of error, not a parameter.
Two habits keep the two straight. First, ask whether every individual in the target population was measured; if not, it is a sample survey, and an estimate, however large. Second, judge accuracy by how the individuals were chosen, not just how many. A biased census (one that systematically misses part of the population through nonresponse) can be less accurate than a small random sample, because random selection protects against systematic tilt while sheer size does not; see parameter vs statistic for the vocabulary that keeps the estimate and the truth apart.
The estimate a survey gives versus the exact value a census gives
A district has 50,000 students. A sample survey draws a simple random sample of 400 students and finds that 240 of them walk or bike to school. Estimate the district proportion and its standard error, and contrast that with what a census would report.
Compute the sample proportion. The statistic is , read as p-hat, the fraction of the sample who walk or bike.
Compute the standard error of , which measures how much the estimate would bounce from sample to sample: .
Fill in the pieces: , then divide by : .
Take the square root: . Check: , which rounds back to 0.0006.
Attach a rough 95% margin using about two standard errors: , so the estimate is , roughly 0.551 to 0.649.
Contrast the census. A census would measure all 50,000 students and report the exact district proportion as a single number, with no standard error and no margin, because nothing was left to chance.
The sample survey estimates that about 60% of students walk or bike, give or take roughly 5 percentage points (standard error about 0.0245). A census would instead report the district's exact proportion with no margin of error, because every student, not a sample, would be measured.
Frequently asked questions
Is a census always more accurate than a sample survey?
No. A census has no sampling error, but it can still suffer nonresponse and missed individuals, which are nonsampling errors. A small random sample, well run, can beat a census that systematically misses part of the population, because random selection guards against tilt that size alone does not.
Is a sample survey an observational study?
Yes. A survey collects data from people using a standard set of questions and imposes no treatment, so it is an observational study. It can describe a population and reveal associations, but on its own it cannot establish cause and effect.
Does a census have a margin of error?
No sampling margin of error, because a census measures the whole population rather than a sample, so its summary is the parameter itself. It can still be wrong through nonsampling problems such as nonresponse or counting mistakes, but those are not captured by a margin of error.