It's not unusual to be unusual (or: A different take on multivariate distributions of personality)

Personality, and many other psychological constructs, are assumed to be distributed along multiple dimensions. The current research demonstrates an intriguing implication that these multidimensional distributions hold: as dimensionality increases, people are located progressively further away from the average. In other words, multivariate models of personality render people to be rather ‘unusual.’ I review the geometric and statistical basis for this phenomenon and then illustrate its occurrence in real life using large, open-source personality data. This research offers a fresh perspective on the behavior of multivariate distributions for those who are interested in personality, psychological testing, or enjoy a lighthearted (but substantial) take on statistics.