define Sampling With and without Replacement in statistics

Sampling With Replacement:

In statistics, sampling with replacement means that each time a sample is taken from the universe or population, it is returned to the universe before the next sample is taken. In other words, each member of the population has an equal chance of being selected each time a sample is taken. This method is used when the population size is small.

For example, if you were to draw a card from a deck of cards, note the result, and then put the card back in the deck before drawing again, you would be sampling with replacement.

Sampling Without Replacement:

On the other hand, sampling without replacement means that once a member of the population has been selected for the sample, it cannot be selected again. Each member of the population may only be selected once. This method is used when the population size is large.

For example, if you were to draw a card from a deck of cards, note the result, and then NOT put the card back in the deck before drawing again, you would be sampling without replacement.