The research (spring of 2008) investigated the understanding of concept of arithmetic mean of 208 4th and 6th grade students of elementary school, in Thessaloniki in Greece. The result agrees with the conceptions of Mokros & Russell (1995, 22) that “the arithmetic mean is a mathematical object of unappreciated complexity”. The students participated in research were able to calculate the mean using the arithmetic algorithm, although they couldn’t use the metre to summarize data neither applied it in real life problems, that is interpreted as absence of statistical thought (Phannkuch & Wild, 2003). Children limit themselves in the simple knowledge of the algorithm (computational knowledge) that constitutes the lower level of instrumental understanding of the concept (Pollatsek et al, 1981). With regard to the comprehension of representativeness students recognized this attribute but they didn’t lead to the confrontation of data as an entity.