Evanthis Chatzivasileiou, Ioannis Michalis, Christina Tsaliki, Io Sakelariou

The arithmetic mean is not only a basic concept of statistics and experimental science but it is the most frequently used concept in everyday life (Pollatsek et al, 1981). The concept of average is related to the comprehension of seven properties of the arithmetic mean (Strauss & Bichler, 1988).

This paper aims to explore the in service elementary school teachers' conceptions of the arithmetic mean. The research took place in December 2010 and investigates the conceptions of the seven properties of the arithmetic mean. A paper & pencil questionnaire has been designed, comprised of ten simple questions which were undertaken by 120 Greek in service elementary school teachers' of Thessaloniki region in Northern Greece. The questionnaires were undertaken in a collective way.

The results show a lack of understanding of some properties like: (a) the sum of deviation from the average is zero, (b) the average does not necessarily coincide with one of the values which are composed by it, (c) the average is a representative value of the data. Another difficulty concerns misunderstanding of the distribution of a data set.

The data analysis revealed that the arithmetic mean is quite complicated to be fully understood (MacCullough, 2007) by the in service teachers even though it seemed that they used it in several occasions.

**Keywords:** statistics; arithmetic mean; education

**Biography:** Elentary school teacher of the Experimental primary school of the Aristotle University of Thessaloniki

Researcher on teaching statistics