Normalverteiltheit

Normalverteiltheit, also known as normality, refers to a property of a dataset or a probability distribution. A dataset is considered normally distributed if its values are symmetrically distributed around the mean, forming a bell-shaped curve when plotted on a histogram. This distribution is characterized by its mean, median, and mode all being equal, and by its symmetry around the mean.

The normal distribution is a fundamental concept in statistics and probability theory. It is often used as a model for various natural phenomena, such as measurement errors, physical characteristics of populations, and financial returns. The normal distribution is also the basis for many statistical tests and methods, such as the t-test and regression analysis.

The normal distribution is defined by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the peak of the bell curve, while the standard deviation determines its width. A smaller standard deviation results in a narrower curve, while a larger standard deviation results in a wider curve.

The normal distribution has several important properties. It is symmetric around the mean, and the probability of a value falling within a certain range can be calculated using the cumulative distribution function. The normal distribution is also closed under linear transformations, meaning that if a variable is normally distributed, then any linear combination of that variable will also be normally distributed.

In practice, it is often assumed that data follows a normal distribution, but this assumption should be tested and validated using appropriate statistical methods. If the data does not follow a normal distribution, alternative methods and distributions may be more appropriate.