The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution centred on the mean, indicating that data around the mean occur more frequently than data far from it. The normal distribution will show as a bell curve on a graph.
The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotic. Around its centre, a normal distribution is exactly symmetrical.
The mean of a standard normal distribution is 0 and the standard deviation is 1. The z distribution is another name for this. The symbol N ( μ , σ ) denotes a normal distribution, with N being the mean of the distribution and S denoting the standard deviation of the distribution.
The numbers are evenly distributed both above and below the mean in a normal distribution. If the mean, mode, and median are all equal, the population has a perfectly normal distribution. The mean, mode, and median for a population of 3,4,5,5,5,6,7 are all 5.
Because the probability density graph of the normal distribution resembles a bell, it is commonly referred to as the bell curve. The Gaussian distribution is named after the German mathematician Carl Gauss, who first characterised it.