The sample is not the population

Abstract

Given sample data, how do you calculate the value of a parameter? While this question is impossible to answer, it is frequently encountered in statistics classes when students are introduced to the distinction between a sample and a population (or between a statistic and a parameter). It is not uncommon for teachers of statistics to also confuse these concepts. An excerpt of a national mathematics examination paper, where a sample is mistaken for the population, is used to illustrate this confusion as well as sample variation and its link to sample size. We discuss two techniques that can be used to explain the difference between a parameter and a statistic. The first is a visual technique in which the variability in calculated statistics is contrasted to the fixed value of the corresponding parameter. Thereafter, we discuss Monte Carlo simulation techniques and explain the contribution that these methods may have.