“Mathematics is about patterns, but the workings of randomness seem to be somewhat removed from patterns. One of the definitions of random can be explained as a lack of appreciable pattern.”
This definition fits when studying the behavior of a single individual, as this can be unpredictable. However, when studying mass behavior, it can be predictable.
The curve in the figure above is known as the Gaussian bell. Abraham de Moivre proposed it in 1730 as an approximation to the binomial distribution that Jacob Bernoulli published a few years earlier. At that time, the probability was seen only as a tool to gain an advantage in games of chance. The precursor of the use of probability for these cases was a gambling scholar named Girolamo Cardano, who applied this knowledge as a sixth sense for the total flow in a game of chance.
By the beginning of the 19th century, probability and its applied branch, statistics, were already used in many other fields, such as astronomy.
The Gaussian bell acquired its iconic status in 1835 when it began to appear in the social sciences. Large amounts of data, such as weights, heights, ages, etc., were distributed in this form. This motivated a scientist named Francis Galton to use statistics for his studies on biological inheritance. He was the first scientist to use statistics in an area other than astronomy. Galton published his studies in 1889, repeatedly obtaining bell-shaped distributions of data and discovering the properties that they concealed.
With the Gaussian bell well established, scientists developed new statistical tools. It became evident that mathematics can apply not only to the physical sciences but also to biology and even to the social sciences.
Today it is a widely used mathematical tool for describing many phenomena, and studying this curve is fundamental for a data scientist.