This mixed methods, sequential, exploratory study addresses the problem, “How significant are statistical representations of ‘average student achievement’ for school administrators as instructional leaders?” Both phases of the study were designed within Charles Sanders Peirce’s pragmatic theory of interpretation. In the first, phenomenological phase, 10 Saskatchewan school principals were each interviewed three times and invited to read aloud three different student achievement reports. Principals generally held a “centre-of-balance” conception for the average, which related to perspectives deriving from their organizational position. Abductive reasoning, a proclivity to act upon “below average” student achievement, leadership through asking leading questions, an inquiry cast of mind, and other pragmatic principles were clearly apparent. No evidence was found that school administrators were constrained by normative statistics into a uniform outlook, nor into purely instrumental behaviour. In a succeeding, overlapping phase based in the psychophysics of perception, Saskatchewan school leaders (principals and vice-principals) (n=210) were randomly assigned to one of four groups and asked to read an achievement report depicting student performance as a distribution of scores on a criterion scale. School leaders’ dispositions to be rational-analytical or intuitive-experiential were measured pre-and post-reading. A MANCOVA revealed small but significant changes in school leaders’ dispositions depending on the way the report was framed. Small but significant interactions between valence and audience on a reader’s rationality were observed. Negatively-framed test scores effected greater changes than positively-framed test scores in diminishing school leaders’ beliefs in their rationality. Principals’ and vice-principals’ dispositions did not differ. I conclude that reading reports which depict student achievements within a normative distribution has little statistical significance in changing leadership practice. However, school principals’ interpretations demonstrate the substantial practical significance of statistics when leading change. School administrators consider average student achievement not with the inferential patterns assumed within contemporary notions of heuristic irrationality, but rather as a reasoned form of inquisitive thinking and behaviour that has been formalized and comprehensively described in North American philosophy for over 100 years.