Reconciling theoretical models with experimental data is a major challenge in neuroscience. We investigate how neurons that exhibit disorderly properties individually can produce orderly collective dynamics. Focusing on continuous-attractor networks, which model representations of continuous variables such as head direction and spatial location, we address the discrepancy between the symmetry required by these models and its apparent absence in mammalian neural recordings. Analysis of mouse head-direction cell tuning curves reveals significant heterogeneity that violates basic assumptions of classical continuous-attractor models. We nevertheless construct network models, using an optimization procedure, that match the observed neuronal responses while exhibiting attractor dynamics. To facilitate the study of larger networks, we develop an effective statistical description of heterogeneous tuning curves that generates artificial data with features in quantitative agreement with the experimental data. We then derive dynamical mean-field equations for the large-network limit that are equivalent to those of classical continuous-attractor models, including an emergent circular symmetry, despite the disorderly responses of individual neurons. We extend the mean-field framework to higher dimensions, applying it to grid cells. Our approach provides a general method for deriving and analyzing population dynamics that are consistent with observed neuronal responses.