# READING LEVELS OF STATISTICAL GRAPHS

P. Arteaga Cezón1, J.M. Vigo2, C. Batanero1

2IES Puertas del Campo (SPAIN)
Statistical graphs are pervasive in our society and can be used to communicate information efficiently, as a tool for data analysis; therefore, the construction and interpretation of statistical graphs is also an important part of statistical literacy. Moreover, the study of statistical graphs is included in compulsory education at the primary and secondary school levels.

Many authors have described different levels of graphical understanding; Bertin (1967) proposed the following levels: B1) Extracting data or direct reading of the data represented on the graph. For example, in a bar graph, reading the frequency associated with a value of the variable; B2) Extracting trends; being able to perceive a relationship between two subsets of data that can be defined a priori or visually in the graph. For example, visually determining the mode of a distribution in a bar graph; B3) Analysing the data structure; comparing trends or clusters and making predictions. For example, in an attached bar graph, analysing the differences in mean and range of two distributions.

A related classification is due to Curcio who defined the following levels:
C1) reading the data (literal reading of the graph without comparing the information contained in it),
C2) reading between the data (interpreting and integrating the data in the graph),
C3) reading beyond the data (making predictions and inferences from the data to information that is not directly reflected in the graph), and
C4)reading behind the data, which consists on judging the method of data collection, and assessing the data validity and reliability, as well as the possible generalization of findings.

In this paper we present an exploratory study to evaluate the reading level reached by 1st and 2nd year Vocational Training students of hairdressing and aesthetics specialty before the formal teaching of the subject. We propose a classification with five reading levels that combines those by Bertin and Curcio and we evaluate the reading level reached by the students using this new classification. The students were given five tasks concerning different graphs (bar graphs, population pyramid, line graph, pie graph and cartogram) and were asked to reply several questions on the same.

Our results suggest that few students reach the upper level of critically reading the graph and the existence of a considerable proportion of students that did not reach the lower levels. We observed a better performance in the 2nd year students, who had studied some statistics the previous year. A conclusion is the need to reinforce the students’ graphical competence in order to make them able to manage in the information society.