Development of an understanding of a sampling distribution

Abstract

This study examined students’ thinking in relation to understanding of sampling distributions. The results found that the understanding of sampling distributions develops through five steps. At the level 0, the students did not perceive sampling variability. At the level 1, the students perceived sampling variability, but they confused data in a sample and the sample statistics as data. At the level 2, the students paid attention to the spread of the sample statistics but were not interested in any central tendency. At the level 3, the students paid attention to the central tendency of the sample statistics as well as the spread of the sample statistics. At the level 4, the students paid attention to the central tendency of the sample statistics as well as the spread of the sample statistics and they understood the relationship between the sample size and sampling variability.