Meaning of Gaussian Bell
The bell concept comes from the late Latin campāna, in turn linked to the Italian region of Campania. Bells were first used there, which are inverted cup-shaped brass instruments that are struck to make a sound. Objects similar in shape to these instruments are also called a bell.
Gauss, for his part, is the surname of a physicist and mathematician (Carl Friedrich Gauss) who was born in 1777 in Brunswick and died in 1855 in Göttingen. His scientific contributions have marked the development of mathematics.
The notion of Gaussian bell refers to the graphical representation of a statistical distribution linked to a variable. This representation is in the shape of a bell.
According to DigoPaul, the Gaussian bell graphs a Gaussian function, which is a kind of mathematical function. This bell shows how the probability of a continuous variable is distributed.
The concept of a mathematical function can be defined as the relationship between two quantities or quantities such that one depends on the value of the other. Each of them must belong to a different set: one is known by the domain name, and the other is called a codomain; each element of the first corresponds only to one of the other.
We can understand mathematical functions with a simple example: the duration of a trip between two geographical points depends on the speed at which the body is moving, which must be included in an equation together with the distance. In this particular case, speed and duration vary inversely: the higher one is, the shorter the other.
Another concept that appears in the context of the Gaussian bell is the continuous variable. To explain it, it is necessary to start by defining a discrete variable, which is one that does not accept an “intermediate” value between those exposed in a given set, but only those that are observed in it; For example, if we want to count the number of people in a room, the result will always be an integer (such as 3 or 4, but never 3.2).
The notion of a continuous variable, on the other hand, does accept these values, and therefore its application is very different. For example, the measurement of the height of a human being yields a variable of this type, and the precision of the result always depends on the instrument used, which is why we must consider a certain margin of error.
In the Gaussian bell, a middle zone (concave and with the mean value of the function in its center) and two extremes (convex and with a tendency to approach the X axis) can be recognized. This distribution shows how the values of variables whose changes are due to random phenomena behave. The most common values appear in the center of the hood and the less frequent, in the extremes.
With the Gaussian bell, for example, the average income of the economically active population of a region X can be analyzed. While there are people in that territory who earn $ 10 per month and others who receive more than 1,000,000, most individuals earn between $ 5,000 and $ 10,000. Those values will be concentrated in the center of the Gaussian bell.
Another name by which the Gaussian bell is known is normal distribution. One of the reasons for its importance is that it is related to a very significant estimation method called least squares, used for a long time to optimize a series of ordered pairs to find a continuous function that most closely approximates them; in simpler terms, given a set of data, this technique seeks to “fit” them to a “clean” line, accepting a certain margin of error.