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Statistical positioning, the localization of nucleosomes packed against a fixed barrier, is conjectured to explain the array of well-positioned nucleosomes at the 5’ end of genes, but the extent and precise implications of statistical positioning in vivo are unclear. We examine this hypothesis quantitatively and generalize the idea to include moving barriers as well as nucleosomes actively packed against a barrier. Early experiments noted a similarity between the nucleosome profile aligned and averaged across genes and that predicted by statistical positioning; however, we demonstrate that aligning random nucleosomes also generates the same profile, calling the previous interpretation into question. New rigorous results reformulate statistical positioning as predictions on the variance structure of nucleosome locations in individual genes. In particular, a quantity termed the variance gradient, describing the change in variance between adjacent nucleosomes, is tested against recent high-throughput nucleosome sequencing data. Constant variance gradients provide support for generalized statistical positioning in about 50% of long genes. Genes that deviate from predictions have high nucleosome turnover and cell-to-cell gene expression variability. The observed variance gradient suggests an effective nucleosome size of 158 bp, instead of the commonly perceived 147 bp.