The recent reform of the teaching of statistics in French secondary schools comes up against two difficulties which this paper tries to analyse. The first one lies in the fact that teachers of mathematics have gradually unlearnt to teach the non-purely mathematical parts of the mathematics curriculum since the so-called « new mathematics » reform, whereas statistics belongs to « mixed » mathematics. The second yet more specific difficulty originates from the fact that statistics mostly deals with variability and uncertainty, two notions usually ignored and even repressed in the worldview shared by most people and institutions.