The Common Core Standards for Mathematical Practice describe mathematical habits of mind foundational for mathematical thinking and understanding. The Statistical Education of Teachers (SET) report, commissioned by the American Statistical Association (ASA), interprets the Mathematical Practices through a statistical lens. In this article, we present tasks focused on variability that can be taught through the lens of Mathematical Practice 6: Attending to Precision (MP6). We show that teacher tasks that focus on variability and its quantification (by computing multiple different measures on different aspects of an entire dataset and constructing arguments), prompts teachers to attend to statistical precision. Additionally, we make the connection that ideas related to variability are present in all components of the statistical investigative process: posing questions that anticipate variability, anticipating variability in data collection, analyzing the variability present, and interpreting the variability to make quantitative statements about error and tasks that aim toward understanding variability require the employment of Statistical MP6.