To obtain population-based inference in the presence of missing data and outliers, we develop a latent class model that assumes each observation belongs to one of K unobserved latent classes, with each latent class having a distinct covariance matrix. The latent class covariance matrix with the largest determinant is assumed to form an "outlier class," and we conduct inference after removing these outliers. As in Ghosh-Dastidar and Schafer (2003), we use multiple imputation to promulgate uncertainty in the outlier status. We extend their work by embedding the outlier class in a larger mixture model, consider various assessments of model choice and fit, and construct the model to account for complex sample designs. We apply our methods to estimate obesity measures in the Healthy For Life Study, a survey of children receiving medical care at community health centers in the eastern US.