Humans readily form social impressions, such as attractiveness and trustworthiness, from a stranger's facial features. Understanding the provenance of these impressions has clear scientific importance and societal implications. Motivated by the efficient coding hypothesis of brain representation, as well as Claude Shannon's theoretical result that maximally efficient representational systems assign shorter codes to statistically more typical data (quantified as log likelihood), we suggest that social "liking" of faces increases with statistical typicality. Combining human behavioral data and computational modeling, we show that perceived attractiveness, trustworthiness, dominance, and valence of a face image linearly increase with its statistical typicality (log likelihood). We also show that statistical typicality can at least partially explain the role of symmetry in attractiveness perception. Additionally, by assuming that the brain focuses on a task-relevant subset of facial features and assessing log likelihood of a face using those features, our model can explain the "ugliness-in-averageness" effect found in social psychology, whereby otherwise attractive, intercategory faces diminish in attractiveness during a categorization task.