Conceptions of sample and their 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 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.