A normal distribution, also known as a Gaussian distribution, is a continuous probability distribution characterized by its bell-shaped curve. It is defined by two parameters: the mean (average) and the standard deviation (which measures the spread of the distribution). The mean determines the center of the distribution, while the standard deviation indicates how spread out the values are around the mean.
In a normal distribution, approximately 68% of the data points fall within one standard deviation of the mean, about 95% fall within two standard deviations, and around 99.7% fall within three standard deviations. This property is often referred to as the empirical rule or the 68-95-99.7 rule.
The normal distribution is significant in statistics and is widely used in various fields such as psychology, finance, and natural sciences because many real-world phenomena tend to approximate a normal distribution. Examples include heights of individuals, test scores, and measurement errors.
Graphically, a normal distribution is symmetrical, meaning that the left and right sides of the curve are mirror images. This symmetry indicates that the mean, median, and mode of the distribution are all equal and located at the center of the distribution.
In addition to these properties, the normal distribution is important in inferential statistics, as it is often assumed for various statistical tests and methods, allowing for the application of the Central Limit Theorem, which states that the means of samples of large enough size will be normally distributed, regardless of the shape of the population distribution.