The Gaussian bell, or Gaussian function, is a mathematical curve used to describe the distribution of data in a population. this curve It is characterized by its symmetrical shape. and for having the highest concentration of data at its central point, which is known as average’. This curve was discovered by the German mathematician Carl Friedrich Gauss in the 19th century, and has since been used extensively in a wide variety of fields, including statistics, physics, engineering, ecology, economics, biology and the empirical sciences.
Meaning of the Gaussian bell in statistics
The Gaussian bell is a graphical representation of the normal distribution, which is one of the most important concepts in statistics. The normal distribution, also known as the Gaussian distribution, is used to describe her distribution of data in a population and is characterized by its symmetrical bell shape.
The Gaussian bell is useful in statistics because it allows us to calculate the probability that a specific value is within a certain range. This probability can calculate using the empirical rulewhich states that in a normal distribution 68% of the data are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and that 99.7% are within three standard deviations from the mean.
The Gaussian bell is also used in the construction of statistical models, since many natural and social phenomena follow a normal distribution. For example, people’s heights, object weights, sustainable development, and scores on standardized tests like the SAT, They usually follow a normal distribution..
What is the Gaussian bell for?
The Gaussian bell is a tool fundamental in statistics and related sciences, since it allows us to understand and analyze the distribution of data in a population. Some of the applications The main features of the Gaussian bell are:
- Describe the data distribution: The Gaussian bell shows how the data is distributed in a population. By plotting the data on a normal curve, you can quickly understand the shape of the distribution, Is it symmetric or asymmetric?and if there are outliers.
- calculate probabilities: The Gaussian bell is used to calculate the probability that a specific value is within a range certain.
- Perform hypothesis tests: In many tests of statistical hypotheses, the Gaussian bell is used as the basis for establishing limits and confidence intervals. For example, if you are comparing two sets of data, you can use the Gaussian bell to determine if there are significant differences among them.
- statistical models: The Gaussian bell is one of the most used distributions for the construction of statistical models. Many natural and social phenomena follow a normal distribution, and the Gaussian bell allows you to create models that fit these distributions.
What are the parts of the Gaussian bell?
The Gaussian bell is a mathematical curve that has its function to describe the distribution of data in a population. This curve is characterized by its symmetrical shape and by having the greater concentration of data at its central point.
Gaussian bell is divided into several partswhich are:
- Central point: This is the highest point of the Gaussian bell and represents the mean or average of the data in the population.
- abscissa axis: This is the horizontal axis of the graph that represents the data values in the population.
- Edge of ordered: This is the vertical axis of the graph that represents the frequency or density of the data in the population.
- Standard deviation: The standard deviation is a dispersion measure indicating how far the data is from the mean. In the Gaussian bell, the standard deviation is shown as the width of the curve.
- Area down the curve: The total area under the Gaussian bell curve is equal to 1which means that it represents the total probability of the data in the population.
- left tail: This is the part of the curve to the left of the mean, and represents the lower values of the data in the population.
- right tail: This is the part of the curve to the right of the mean, and represents the higher values of the data in the population.
What is the significance of the Gaussian bell?
The Gaussian bell provides a way to describe the distribution of data in a population and understand their behavior. Besides:
- Allows you to understand the distribution of data: The Gaussian bell shows how the data is distributed in a population, and allows to identify if this distribution Is it symmetric or asymmetric?, and if there are outliers. This is essential to be able to interpret the data and make decisions based on it.
- Helps calculate probabilities: The Gaussian bell is used to calculate probabilities of events in the population, which is very useful for making predictions and making decisions. The standard normal curve has specific propertieswhich allow it to be used to calculate the probability that a specific value is within a certain range.
- Allows for statistical tests: The Gaussian bell is the basis of many statistical tests, such as the Student’s t-test and the Fisher’s F-test. These tests are used to compare data and determine if there are significant differences between them.
- Serves as a model for many natural and social phenomena: Many natural and social phenomena follow a normal distribution, which allows the use of the Gaussian bell to create statistical models that allow understand and predict their behavior.
How to understand the Gaussian bell? – Interpretation
To understand the Gaussian bell it is important to take into account its characteristic shape, which is symmetric, and with the highest concentration of data at its central point (the mean). The interpretation of the Gaussian bell can be done as follows:
- He highest point of the curve represents the mean of the data. This means that most of the data is around this value.
- The standard deviation of the curve represents the spread of the data around the mean. The larger the standard deviation, the more spread out the data will be.
- The curve is divided into two parts symmetric on both sides of the mean. These parts represent the lowest and highest values of the data in the population.
- He total area under the curve is equal to 1, which represents the total probability of the data in the population. The probability that a specific value falls within a given range can be calculated using the Gaussian bell curve.
- The Gaussian bell can be used to identify outliers in the population. Values that are very far from the mean may be considered outliers and may affect the interpretation of the data.
What is the history of the Gaussian bell?
The Gaussian bell, also known as the normal distribution, owes its name to the German mathematician and astronomer Johann Carl Friedrich Gauss, who described it in the eighteenth century.
However, the normal distribution was first discovered by Abraham de Moivre, an 18th century French mathematician. Moivre studied the distribution of errors in the measurement of astronomical data and discovered that the distribution of these errors followed a symmetrical bell shape.
Years later, in 1809, Gauss published a work in which he described the normal distribution in a more complete and formal way. Gauss used the normal distribution to model the distribution of errors in the measurement of astronomical and geodetic data. Since then, the normal distribution It has been widely used in statistics.natural sciences, social sciences and other disciplines, because many natural and social phenomena follow this distribution.