Born as a tool for handling measurement errors in astronomy, in the nineteenth century the normal curve invaded the human and biological sciences. Two names are tied to this transformation: the Belgian Adolphe Quetelet and the Englishman Francis Galton.
Quetelet and the “average man”
Around 1835 Adolphe Quetelet had a bold idea: to apply the methods of astronomical statistics to human beings. Collecting data on height, weight and other measurements of large populations, he observed that these were distributed exactly according to the Gaussian bell. From this he drew the concept of the homme moyen, the “average man”: a fictitious individual whose characteristics coincide with the mean of the population, around which individuals scatter with a certain standard deviation (Stigler). It was also Quetelet who introduced the body mass index (the ratio ), still known today as the Quetelet index.
Galton and regression
At the end of the century Francis Galton, a cousin of Charles Darwin, studied heredity by measuring the height of parents and children. He noticed a curious phenomenon: the children of very tall parents tended on average to be shorter than their parents, and the children of very short parents taller — a return toward the population mean. He called this effect regression toward the mean, a term that is at the origin of today’s regression analysis (Stigler; Boyer). To visualise how many small random causes generate the bell, Galton built the quincunx (or “Galton board”): a tilted board on which balls, bouncing off rows of pins, pile up at the bottom, spontaneously tracing out a normal distribution.
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Topics: Distribuzioni probabilita
Concepts: Distribuzione normale · Deviazione standard · Valore atteso
People: Adolphe Quetelet · Francis Galton