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Cell heterogeneity and the inherent complexity due to the interplay of multiple molecular processes within the cell pose difficult challenges for current single-cell biology. We introduce an approach that identifies a disease phenotype from multiparameter single-cell measurements, which is based on the concept of "supercell statistics", a single-cell-based averaging procedure followed by a machine learning classification scheme. We are able to assess the optimal tradeoff between the number of single cells averaged and the number of measurements needed to capture phenotypic differences between healthy and diseased patients, as well as between different diseases that are difficult to diagnose otherwise. We apply our approach to two kinds of single-cell datasets, addressing the diagnosis of a premature aging disorder using images of cell nuclei, as well as the phenotypes of two non-infectious uveitides (the ocular manifestations of Beh\c{c}et's disease and sarcoidosis) based on multicolor flow cytometry. In the former case, one nuclear shape measurement taken over a group of 30 cells is sufficient to classify samples as healthy or diseased, in agreement with usual laboratory practice. In the latter, our method is able to identify a minimal set of 5 markers that accurately predict Beh\c{c}et's disease and sarcoidosis. This is the first time that a quantitative phenotypic distinction between these two diseases has been achieved. To obtain this clear phenotypic signature, about one hundred CD8+ T cells need to be measured. Beyond these specific cases, the approach proposed here is applicable to datasets generated by other kinds of state-of-the-art and forthcoming single-cell technologies, such as multidimensional mass cytometry, single-cell gene expression, and single-cell full genome sequencing techniques., Comment: 22 pages, 4 figures. To appear in PLOS Computational Biology