We all know that gene expression occurs within cells, yet we do not think of expression in terms of its fundamental unit -- a single cell. Instead, we understand the expression of genes in terms of a cell population as all of our information comes from samples containing millions of cells. From a complex mixture of cells, we attempt to infer the probable state of an average cell in the population. In truth, what we obtain is an averaged cell, a contrivance for representing biological knowledge beyond the limits of detection. We never know the variation among the members of the population that our methods average into a mean. Recent technological advances allow the precise measurement of single-cell transcriptional states to study this variability more rigorously. How genes are expressed in the population is strikingly different to what we have assumed from extrapolating to an average cell. Does the average cell actually exist? As we discuss, it is becoming increasingly clear that it doesn't.