Students' scheme-based understanding of sampling distributions and its relationship to statistical inference

We distinguish two conceptions of sample and sampling that emerged in the context of a teaching experiment conducted in a high school statistics class. In one conception "sample as a quasi-proportional, small-scale version of the population" is the encompassing image. This conception entails images of repeating the sampling process and an image of variability among its outcomes that supports reasoning<br>about distributions. In contrast, a sample may be viewed simply as "a subset of a population"- an encompassing image devoid of repeated sampling, and of ideas of variability that extend to distribution. We argue that the former conception is a powerful one to target for instruction.