---
title: "Francis Galton"
chunk: 7/9
source: "https://en.wikipedia.org/wiki/Francis_Galton"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:06:17.894886+00:00"
instance: "kb-cron"
---

=== The questionnaire ===
Galton's inquiries into the mind involved detailed recording of people's subjective accounts of whether and how their minds dealt with phenomena such as mental imagery. To better elicit this information, he pioneered the use of the questionnaire. In one study, he asked his fellow members of the Royal Society of London to describe mental images that they experienced. In another, he collected in-depth surveys from eminent scientists for a work examining the effects of nature and nurture on the propensity toward scientific thinking.

=== Variance and standard deviation ===
Core to any statistical analysis is the concept that measurements vary: they have both a central tendency, or mean, and a spread around this central value, or variance. In the late 1860s, Galton conceived of a measure to quantify normal variation: the standard deviation.
Galton was a keen observer. In 1906, visiting a livestock fair, he stumbled upon an intriguing contest. An ox was on display, and the villagers were invited to guess the animal's weight after it was slaughtered and dressed. Nearly 800 participated, and Galton was able to study their individual entries after the event. Galton stated that "the middlemost estimate expresses the vox populi, every other estimate being condemned as too low or too high by a majority of the voters", and reported this value (the median, in terminology he himself had introduced, but chose not to use on this occasion) as 1,207 pounds. To his surprise, this was within 0.8% of the weight measured by the judges. Soon afterwards, in response to an enquiry, he reported the mean of the guesses as 1,197 pounds, but did not comment on its improved accuracy. Recent archival research has found some slips in transmitting Galton's calculations to the original article in Nature: the median was actually 1,208 pounds, and the dressed weight of the ox 1,197 pounds, so the mean estimate had zero error. James Surowiecki uses this weight-judging competition as his opening example: had he known the true result, his conclusion on the wisdom of the crowd would no doubt have been more strongly expressed.
The same year, Galton suggested in a letter to the journal Nature a better method of cutting a round cake by avoiding making radial incisions.

=== Experimental derivation of the normal distribution ===

Studying variation, Galton invented the Galton board, a pachinko-like device also known as the bean machine, as a tool for demonstrating the law of error and the normal distribution.

=== Bivariate normal distribution ===
He also discovered the properties of the bivariate normal distribution and its relationship to correlation and regression analysis.

=== Correlation and regression ===

In 1846, the French physicist Auguste Bravais (1811–1863) first developed what would become the correlation coefficient. After examining forearm and height measurements, Galton independently rediscovered the concept of correlation in 1888 and demonstrated its application in the study of heredity, anthropology, and psychology. Galton's later statistical study of the probability of extinction of surnames led to the concept of Galton–Watson stochastic processes.
Galton invented the use of the regression line and for the choice of r (for reversion or regression) to represent the correlation coefficient.
In the 1870s and 1880s he was a pioneer in the use of normal theory to fit histograms and ogives to actual tabulated data, much of which he collected himself: for instance large samples of sibling and parental height. Consideration of the results from these empirical studies led to his further insights into evolution, natural selection, and regression to the mean.

=== Regression toward the mean ===
Galton was the first to describe and explain the common phenomenon of regression toward the mean, which he first observed in his experiments on the size of the seeds of successive generations of sweet peas.
The conditions under which regression toward the mean occurs depend on the way the term is mathematically defined. Galton first observed the phenomenon in the context of simple linear regression of data points. Galton developed the following model: pellets fall through a quincunx or "bean machine" forming a normal distribution centred directly under their entrance point. These pellets could then be released down into a second gallery (corresponding to a second measurement occasion). Galton then asked the reverse question "from where did these pellets come?"

The answer was not "on average directly above". Rather it was "on average, more towards the middle", for the simple reason that there were more pellets above it towards the middle that could wander left than there were in the left extreme that could wander to the right, inwards.

=== Theories of perception ===
Galton went beyond measurement and summary to attempt to explain the phenomena he observed. Among such developments, he proposed an early theory of ranges of sound and hearing, and collected large quantities of anthropometric data from the public through his popular and long-running Anthropometric Laboratory, which he established in 1884, and where he studied over 9,000 people. It was not until 1985 that these data were analysed in their entirety.
He made a beauty map of Britain, based on a secret grading of the local women on a scale from attractive to repulsive. The lowest point was in Aberdeen.

=== Differential psychology ===

Galton's study of human abilities ultimately led to the foundation of differential psychology and the formulation of the first mental tests. He was interested in measuring humans in every way possible. This included measuring their ability to make sensory discrimination which he assumed was linked to intellectual prowess. Galton suggested that individual differences in general ability are reflected in performance on relatively simple sensory capacities and in speed of reaction to a stimulus, variables that could be objectively measured by tests of sensory discrimination and reaction
time. He also measured how quickly people reacted which he later linked to internal wiring which ultimately limited intelligence ability. Throughout his research Galton assumed that people who reacted faster were more intelligent than others.