Leeds researchers reinvent a classic tool for modern statistics
A new statistical simulator inspired by the famous Galton Board has been unveiled at Leeds during celebrations marking the 50th anniversary of the Leeds Annual Statistical Research (LASR) Workshops.
The workshops were started by Professor Kanti Mardia OBE, who was appointed Chair of Applied Statistics at Leeds in 1973 and served as Head of the Department of Statistics from 1976 to 2000.
Now a Senior Research Professor in the School of Mathematics, Kanti established LASR as a biennial event to foster interdisciplinary research in statistics. During the last five decades it has grown into an established international conference that brings together researchers from a range of scientific disciplines.
The device was formally unveiled by Pro-Vice-Chancellor: Research and Innovation Professor Nick Plant, who said: “This innovative simulator demonstrates how research at Leeds continues to push the boundaries of knowledge while finding new ways to make complex ideas accessible and engaging.
“By building on a scientific concept that has inspired generations of statisticians, our researchers have created a modern tool that deepens understanding of uncertainty, variation and data, concepts that underpin advances across fields from health and climate science to artificial intelligence.”
Invented in the late 19th century, Francis Galton used the Galton Board in his Royal Society lectures to demonstrate the normal distribution. As balls pass through a triangular arrangement of pins and collect in bins below, they form the familiar bell-shaped pattern that shows how randomness and variation create statistical structure. More than 150 years later, it remains a widely used teaching tool in schools and universities worldwide.
Kanti developed the new cylindrical device with researchers Colin Goodall and John Rubo, adding a new dimension to Galton’s classical construction.
Pro-Vice Chancellor: Research and Innovation Nick Plant was on hand to unveil the machine.
By wrapping the outcome space around a circle, it illustrates what to expect when working with circular data and provides an intuitive way of visualising patterns that repeat over time.
These include seasonal changes in climate, daily biological rhythms and monthly cycles studied in health sciences. The device helps demonstrate the statistical methods used to understand such patterns across a wide range of disciplines.
Kanti said: “The simulator represents a fitting innovation for the landmark LASR anniversary, connecting historical probability demonstrations with modern geometric and directional statistics.”
The device also has potential for wider public engagement. The classical Galton Board is already exhibited at MathsCity, Leeds’ interactive mathematics discovery centre, and the cylindrical version would provide a modern companion to the Victorian invention.
Kanti added: “Looking ahead, there are plans to exhibit the cylindrical device at MathsCity, incorporate it into A-level enrichment events and develop a web-based simulator to help students and educators explore the statistical concepts behind the device. These initiatives aim to extend its reach beyond the University and into the wider educational community.”
More details about the development are available in the team’s research paper, published in the Journal of the Royal Statistical Society.
Colleagues can also watch a video of the cylindrical Galton Board in action.
Further information
- Article originally written and published by Tom Vegeris.
- For media enquiries, please contact Faculty Communications Manager Matt Gardner at M.D.Gardner@leeds.ac.uk.
