Secondary school students’ understanding the expected value and variability of sample proportion

Abstract

We analyse secondary school students’ intuitive understanding of the relationships between the population proportion and the expected value of a sample proportion, as well as its variability in relation to the sample size. We propose to 302 students four items in each of which four probable values for the number of outcomes for a given event are requested and in which the proportion population and sample size are varied. The statistical analysis of the values provided by the students suggests a good understanding of the relationships between the population and sample proportions. The variability of the sample proportion is overestimated in big samples and depends on the problem context in small samples. We also observed the equiprobability, positive and negative recency biases.