Understanding how genes coordinate their expression across cells in a growing embryo can provide insights into the transcriptional programs that control development. Intercellular variability of gene expression reflects how consistent expression levels are between cells of the same embryo. An analysis of expression variability can therefore identify which genes are consistently or heterogeneously expressed in a population of cells, and provides a window into regulatory control. Using an analysis of previously published single-cell RNA-seq data set on embryos at collected at different developmental stages, we have identified a putative set of gene expression markers of morulae and blastocyst stages based on changes in intercellular variability. We highlight how genes with extreme levels of variability are enriched for distinct functions and pathways; lowly variable genes operate in maintenance pathways such as protein synthesis, gene expression and cell cycle while highly variable genes tend to be involved in metabolism. Our results suggest that genes with critical and survival roles for the cell are expressed stably while those related to specialized functions are have variable inter-cellular expression. We identified genes with invariant expression across the development stages; such genes fall clearly into three categories of modes corresponding to off, on and highly activated levels of expression. Genes switched on are involved in critical regulatory pathways like EIF2 signaling, protein ubiquitination and mTOR signaling. Genes that are consistently off function in the development of specialized cell types and metabolites. Overall, our analysis suggests new regulators involved in controlling the development of human embryos that would have otherwise been missed using methods that focus on average expression levels and highlight the value in studying expression variability.