Sampling is a fundamental idea in statistical inference due to its potential to make population estimates to which a sample design was applied; however, it has received little attention in educational research, mainly in Spain, where the teaching of stochastic sense is organized into three content groups (data organization and analysis, uncertainty, and inference). Thus, the study of sampling begins in primary education (focused on inference) and deepens into its properties (representativeness and variability) during secondary education.

We aimed to analyze the definitions and examples of these concepts (sample and population) from a sample of 104 students from the first to fourth year of secondary school (12-15 years old) from the same educational centre. We used questions adapted from previus research: “Have you ever heard the words: sample and population? Explain the meaning of each of these words” (item 1) and “Write an example of a situation in which a sample needs to be used and indicate what the sample is and what population it was taken from.” (item 2). Furthermore, the reliability of students’ answers coding using content analysis was ensured through systematic reviews by two researchers and several authors discussing to find agreement on discordant cases.

Although the percentage of students who did not define both concepts was low, it was difficult to provide a correct definition (regardless of educational level), especially for the concept of population, because 89.4% of students defined it as a place where people live. The most common answer was defining both concepts together incorrectly (41 students, 39.4% of the total sample), followed by responses where the population is defined incorrectly and the sample is defined partially correctly (23 students, 22.1% of the total sample) or imprecisely (19 students, 18.3% of the total sample).

In general, students did not correctly identify the population in their proposed examples, even though the sample had been correctly identified. That tendency was much more pronounced in examples referring to homogeneous populations, as well as to 1st year students, where the highest proportion of answers failed to identify both concepts in the proposed examples.

Our insights are fairly worrying, taking into account previous research. We concluded the need to improve the teaching and learning of these concepts from primary education, since most students had difficulty identifying them in situations even proposed by themselves, especially the population concept, which was generally defined as a place where people live. In addition, there is no evidence of improvement as the school year progresses, and the proportion of examples where the sample refers to homogeneous populations is excessive.

Keywords: Sample and population, definition, example, secondary education.