What sampling method allows for the same piece of data to be selected multiple times?

The correct approach involves sampling with replacement, a method where each data point selected is returned to the pool from which samples are drawn before the next selection. This means that it is possible for the same piece of data to be selected more than once in the sampling process, which is a defining characteristic of this method.

Sampling with replacement is particularly useful in situations where retaining the same population size is important or when the researcher wants to ensure that all possible samples can be considered, leading to richer, more varied outcomes in analyses such as statistical inference.

In contrast, the other sampling methods do not allow for this repeated selection from the same dataset. For example, random sampling involves selecting unique observations where each selected item is not returned to the pool. Stratified sampling divides the population into subgroups and samples uniquely from each subgroup without replacement. Systematic sampling selects items based on a fixed interval after an initial selection, also ensuring uniqueness among the items selected.

Thus, sampling with replacement stands out as the only option that permits multiple selections of the same data point in the sampling process.