Gausseloszlás

Gausseloszlás, often translated as Gaussian distribution or normal distribution, is a fundamental concept in probability theory and statistics. It describes a continuous probability distribution characterized by its bell-shaped curve. This shape arises because the data points tend to cluster around a central value, with the frequency of occurrence decreasing symmetrically as one moves further away from this center. The distribution is defined by two key parameters: the mean (μ), which determines the location of the center of the bell, and the standard deviation (σ), which quantifies the spread or variability of the data. A smaller standard deviation indicates that the data points are tightly clustered around the mean, resulting in a narrower, taller bell curve, while a larger standard deviation leads to a wider, flatter curve.

The Gaussian distribution is ubiquitous in nature and many real-world phenomena exhibit this characteristic. For instance, measurements of physical quantities like height, weight, or blood pressure in a large population often follow a normal distribution. It also appears in fields such as finance, where stock price movements can be approximated by a normal distribution, and in signal processing, where random noise is frequently modeled as Gaussian. The mathematical formula for the probability density function of a Gaussian distribution is given by f(x | μ, σ) = (1 / (σ * sqrt(2π))) * exp(-((x - μ)^2) / (2σ^2)). This formula allows for the calculation of the probability of observing a value within a specific range.