Much of the early history of social statistics, strongly influenced by Quetelet, can be viewed as a search for the “average man” – that improbable man without qualities who could be comfortable with his feet in the ice chest and his hands in the oven. Some of this obsession can be attributed to the seductive appeal of the Gaussian law of errors. Everyone, as Poincaré famously quipped, believes in the normal law of errors: the theorists because they believe it is an empirical fact, and the empiricists because they believe that it is a mathematical theorem. Once in the grip of this Gaussian faith, it suffices to learn about means. But sufficiency, despite all its mathematical elegance, should be tempered by a skeptical empiricism: a willingness to peer occasionally outside the cathedral of mathematics and see the world in all its diversity.

There have been many prominent statistical voices who, like Galton, reveled in the heterogeneity of statistical life – who resisted proposals to throw the mountains of Switzerland into its lakes. Edgeworth (1920) mocked excessive reliance on “reasoning with the aid of the gens d'arme's hat – from which, as from the conjuror's, so much can be extracted.” Models for the conditional mean in which independently and identically distributed Gaussian “lerrors” are tacked on almost as an afterthought are rife throughout the realms of science. They are indispensable approximations in many settings. We have argued that it is sometimes useful to deconstruct these models, complementing the estimation of models for the conditional mean with estimates of a family of conditional quantile functions.