Grade 6 (modal age 11) students invented and revised models of the variability generated as each measured the perimeter of a table in their classroom. To construct models, students represented variability as a linear composite of true measure (signal) and multiple sources of random error. Students revised models by developing sampling distributions of model-generated statistics to judge model fit and validity. After instruction, interviews with 12 students were conducted to learn how they conceived of relations among chance, modeling, and inference. Most students' inferences were guided by a hierarchical image of sample, a perspective constituted through their understandings of modeling variability as signal and noise.