Galton board
Galton designed it to illustrate his idea of regression to the mean,[2] which he called "reversion to mediocrity" and made part of his eugenist ideology.
[5] The Ford Museum machine was displayed at the IBM Pavilion during 1964-65 New York World's Fair, later appearing at Pacific Science Center in Seattle.
[9] A board for the log-normal distribution (common in many natural processes, particularly biological ones), which uses isosceles triangles of varying widths to 'multiply' the distance the bead travels instead of fixed sizes steps which would 'sum', was constructed by Jacobus Kapteyn while studying and popularizing the statistics of the log-normal in order to help visualize it and demonstrate its plausibility.
[11] There is also an improved log-normal machine that uses skewed triangles whose right sides are longer, and thus avoiding shifting the median of the beads to the left.
Varying the rows will result in different standard deviations or widths of the bell-shaped curve or the normal distribution in the bins.
Another interpretation more accurate from the physical view is given by the Entropy: since the energy that is carried by every falling bead is finite, so even that on any tip their collisions are chaotic because the derivative is undefined (there is no way to previously figure out for which side is going to fall), the mean and variance of each bean is restricted to be finite (they will never bound out of the box), and the Gaussian shape arises because it is the maximum entropy probability distribution for a continuous process with defined mean and variance.
The rise of the normal distribution could be interpreted as that all possible information carried by each bean related to which path it has travelled has been already completely lost through their downhill collisions.
His goal was to promote the use of ranking instead of measurement in statistics, so that qualities such as intelligence could be assigned numbers without requiring experimental data.
Whenever a large sample of chaotic elements are taken in hand and marshalled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.
Aware of this issue, he tried to address it in 1875 by arguing that his box did not reflect situations where bias would be introduced by what he called a main influence factor.
