This communication describes a subset of results in the field of statistics education, from a larger study that explores teacher's knowledge for teaching mathematics. It focuses specifically on the conceptual understanding of the arithmetic mean and it was developed with two clusters of teachers: 19 elementary teachers (6-11 years old students) and 18 middle school teachers (12-14 years old students) both enrolled in teacher development programmes. Results of this study show several teachers' misconceptions and indicate that they are not prepared to teach arithmetic mean with a deep understanding for conceptual learning.