Which parameters define a normal distribution?

A normal distribution is characterized by two specific parameters: the mean (μ) and the standard deviation (σ). The mean determines the center of the distribution, indicating where the peak of the bell curve lies, while the standard deviation measures the spread or dispersion of the data around the mean. In a normal distribution, the data are symmetrically distributed, and the majority of observations fall within a certain range around the mean, specifically within one, two, or three standard deviations.

The relationship between these two parameters fully describes the shape and characteristics of the normal distribution. Specifically, a larger standard deviation results in a wider and flatter curve, whereas a smaller standard deviation produces a steeper and narrower curve. This distinction is crucial for understanding how data behaves in a normal distribution and for applying statistical methods effectively.

While other parameters like median and mode, or concepts such as probability and frequency, relate to statistical distributions in general, they do not define the characteristics of the normal distribution specifically. The mean and variance can provide insights into a distribution but do not fully capture its shape in the same way that the mean and standard deviation do. Therefore, the combination of mean and standard deviation is the defining feature of a normal distribution.