Sampling with replacement is a method where each item in the population can be selected more than once, because every chosen item is "put back" before the next draw. On AP Stats it appears in Topic 3.3 (DAT-2.C.1) and explains why selections stay independent from draw to draw.
Sampling with replacement means that after you select an item from the population, it goes back into the pool before the next selection. The same individual can show up in your sample two, three, or more times. The CED defines it directly in DAT-2.C.1: when an item can be selected only once, that's sampling without replacement; when an item can be selected more than once, that's sampling with replacement.
Here's the intuition. Imagine drawing names from a hat. With replacement, you read the name, toss it back, shake the hat, and draw again. Every draw faces the exact same population, so the probability of picking any individual never changes. That's the whole appeal for statisticians, because each draw is independent of the ones before it. Without replacement, the hat shrinks each time, the probabilities shift slightly, and the draws are no longer independent. In practice, most real surveys sample without replacement (you don't interview the same person twice), but the math of inference is built on the with-replacement, independent-draws picture.
This term lives in Topic 3.3 (Random Sampling and Data Collection) in Unit 3. It directly supports learning objective AP Stats 3.3.A, identifying a sampling method from a study description, and AP Stats 3.3.B, explaining why a sampling method is or isn't appropriate for a situation. The CED even bakes it into the simple random sample mechanism, where you number individuals and use a random number generator, "ignoring repeats." Ignoring repeats is just sampling without replacement in disguise.
The bigger payoff comes later. The standard formulas for sampling distributions in Units 5-7 assume independent observations, which technically requires sampling with replacement. Since real samples are taken without replacement, AP Stats patches the gap with the 10% condition. As long as your sample is less than 10% of the population, removing items barely changes the probabilities, so without-replacement sampling behaves almost exactly like with-replacement sampling. Understanding this term is understanding why that condition exists at all.
Keep studying AP Statistics Unit 3
Sampling Without Replacement (Unit 3)
These are two halves of one CED statement (DAT-2.C.1). The only difference is whether a selected item goes back in the pool. With replacement keeps draws independent; without replacement makes each draw depend slightly on the previous ones.
Random Sampling and the SRS (Unit 3)
The standard SRS mechanism, numbering individuals and using a random number generator while ignoring repeats, is sampling without replacement. If you kept the repeats instead of ignoring them, you'd be sampling with replacement. Same tool, different rule about duplicates.
Independence and the 10% Condition (Units 5-7)
Standard error formulas assume independent draws, which is the with-replacement world. Real samples are without replacement, so you check that the sample is under 10% of the population. When the sampling fraction is that small, the two methods give nearly identical results.
Sample Size and Variance (Units 3 & 5)
When the sample is a large chunk of a small population, the method matters. Sampling with replacement produces a larger variance for a sample proportion than sampling without replacement, because without replacement, each draw gives you information you can't get twice.
This is mostly a multiple-choice concept. Expect stems that describe a selection process and ask you to identify whether it's with or without replacement (learning objective 3.3.A), or stems that ask when the distinction actually matters for inference (3.3.B). Practice questions hit it from a few angles, like estimating a mean from 5,000 households when the sampling fraction is small (answer: the two methods are practically equivalent), or selecting 3 items from only 100 (answer: with replacement gives the larger variance of the sample proportion). The distinction is most critical when the sample is a big fraction of a small population.
It also shows up through bootstrap resampling, which works by resampling from your data with replacement to estimate a sampling distribution. On FRQs, you won't usually see the phrase verbatim, but it's lurking whenever you justify the independence condition. Writing "the sample is less than 10% of the population, so observations can be treated as independent" is you handling the with-versus-without-replacement issue for points.
With replacement, a selected item goes back in the pool and can be chosen again, so every draw has identical probabilities and draws are independent. Without replacement, each item can be selected only once, so the pool shrinks and probabilities shift with each draw. Almost all real surveys sample without replacement, but inference formulas assume with-replacement behavior. The 10% condition is the bridge: when the sample is under 10% of the population, the difference is negligible.
Sampling with replacement means a selected item returns to the population and can be chosen again, while sampling without replacement allows each item to be picked only once (DAT-2.C.1).
With replacement, every draw is independent because the population never changes between selections.
The standard SRS mechanism of generating random numbers and ignoring repeats is sampling without replacement.
When the sample is less than 10% of the population, sampling without replacement behaves almost exactly like sampling with replacement, which is why the 10% condition justifies treating observations as independent in inference.
Sampling with replacement gives a larger variance for a sample statistic than sampling without replacement, and the gap is biggest when the sample is a large fraction of a small population.
Bootstrap resampling is built on sampling with replacement: you resample your own data, allowing repeats, to estimate a sampling distribution.
It's a sampling method where each selected item goes back into the population before the next draw, so the same individual can appear in the sample more than once. The AP CED defines it in Topic 3.3 under essential knowledge DAT-2.C.1.
With replacement, an item can be selected multiple times and every draw is independent. Without replacement, each item can be chosen only once, so the population shrinks and probabilities change slightly with each draw.
Only when the sample is a large fraction of the population. If you're sampling 3 items out of 100, the methods give noticeably different variances, but sampling a few hundred households out of 5,000 makes the two practically equivalent. That's the logic behind the 10% condition.
Without replacement. The CED's own SRS mechanism says to number individuals, use a random number generator, and ignore repeats, which means no one can be selected twice.
Bootstrapping resamples from your original data to estimate a sampling distribution. You must allow repeats, because resampling n items from n items without replacement would just hand you back the exact same dataset every time.