Abstract:

The median is a measure of central position that is preferable to the mean in the presence of outliers and skewed distributions, and has wide use in nonparametric inference, which is used in small samples, ordinal or non-normal data. Although assumed to be simple, previous research has described numerous calculation and interpretation errors, including the following:
a) failure to recognize situations in which the median should be used instead of the mean;
b) confusing the symbolic representation of the median or confusing mean and median;
c) failure to understand the effect of an outlier on the median; and
d) calculating the median without taking into account the frequency of the data.

Previous researches has been conducted with elementary or secondary school students or with future elementary school teachers, and there are no precedents with university students.

To fill this gap, an evaluation study was carried out at the University of Granada with university students who were participating in a statistics course, using the ontosemiotic approach to mathematical cognition and instruction as a theoretical framework.

The sample consisted of 148 students who were studying the Statistics course (2nd year) of the Degree in Physical Activity and Sport Sciences at the University of Granada. The questionnaires were applied after the subject had been explained in the aforementioned course, which is the first course of mathematical content in the degree. In this paper we present only the results of the first task, which analyzes the calculation of the median for an odd and even number of data and whether students choose the mean or the median to represent the given data.

The responses to each section of the items were classified by a cyclical and inductive process, typical of content analysis, into correct or incorrect responses and, within the latter, the errors found were classified. According to the ontosemiotic approach, these errors are interpreted as semiotic conflicts that can be conceptual, procedural or notational.

73% of the students calculated correctly the median in an odd data set and 76.4% in an even data set. The main semiotic conflicts encountered in the calculation of this measure consisted of not ordering the data, confusing the median with the order number in the ordered data set, or not resolving the indeterminacy.

On the other hand, only 40% chose correctly the median as the best representative of the data when there is an outlier. The main conflicts encountered in this task were thinking that the variability of the data does not affect the mean, not perceiving the effect of the outlier on the mean or thinking that, in any case, the mean is the best representative of the data.

Although the results corresponding to the calculation are better than the ones reported in research with high school students, there is not much difference in terms of the appropriate choice between mean and median according to the situation. The students' answers confirm the semiotic conflicts identified in previous research and, in addition, show some new ones not taken into account in those studies.

Consequently, it will be necessary to take into account these difficulties in the statistical training of Physical Activity and Sport Science students and replicate the work to see if these difficulties are also shared in other degree programs.

Keywords:

Assessment, statistics, median, university students.