Two strands of research motivate this study. One is the interest in school students' development of understanding of the concept of average, historically part of the mathematics curriculum and prominent in the statistics curriculum introduced in the early 1990s. The other is the belief of some educators that students learn meaningfully when experiencing cognitive conflict that challenges incorrect or incomplete understandings. This study presented 58 students in Grades 3, 6, and 9 with a series of questions about the concept of average. After initial levels of response were observed, students were presented with alternative responses on video from other school students and asked to choose which best resolved the task at hand. Initial responses confirmed the levels of understanding in an earlier study based on the same questions. Responses after the experience of cognitive conflict were either at the same level as before or higher, with no student finally agreeing with a lower level response. The results are compared with longitudinal change in relation to average and change resulting from cognitive conflict in relation to other areas of chance and data. Implications of the research are considered.