Understanding sampling by Chilean secondary school students

Abstract

In statistical inference, importance of sampling is recognized as one of its key concepts, which has allowed its incorporation internationally in different curricular guidelines and specifically in the Chilean curriculum, since the first notions of sampling are introduced in 7th Grade. This paper presents an analysis of the responses to an open-ended written questionnaire, designed to evaluate understanding of sampling, that was applied to a sample of 1,241 Chilean secondary students of 8th, 10th and 12th Grades in six different secondary schools. A mixed methodology was used, with qualitative description of responses and a quantitative analysis of their frequencies. The results reflect outstanding difficulties in the use of elements related to sampling and its properties in different problem situations. For example, students can distinguish the concept of sample in contexts close to their experiences; but when faced with different sampling methods, they are not able to identify biases associated to sample selection. Thus, when deciding if a sample is representative, they mostly identify cases in which the given sample is not.