In order to study the manifestation of data sense and identify ways of thinking about variability in authentically realistic problems in a group of Chilean fifth-grade students, a lesson plan was designed and implemented, within the framework of statistical literacy and using the "lesson study" modality, in which students were urged to make inferences based on the analysis of data corresponding to the tsunami that struck the Chilean coast in 2010. This article focuses on the qualitative study of the data representations produced by two groups of students during the implementation of the lesson plan. The analysis of the behavior of the tsunami carried out by the students led them to work simultaneously with nominal qualitative, ordinal qualitative, discrete quantitative, and continuous quantitative variables; to create new variables; to construct representations of data (multiple bar graphs and frequency tables); and to make inferences based on the data. We conclude that the use of an authentic context and the construction of their own representations promoted data sense in students and facilitated the development of their statistical thinking, through which they were able to recognize, describe, and explain the variability of the phenomenon.