Normal distribution: The prominent probability distribution in statistics
The pattern of distribution of data that take a form of bell-shaped curve is called ‘Normal distribution’. This distribution is also called the ‘Gaussian distribution’ in honour of a famous German mathematician Carl Friedrich Gauss who described it in a monograph published in 1809. This is sometimes also referred as ‘Gauss-Laplacian distribution’ to honour Pierre-Simon Laplace, a French mathematician who made significant contributions in formulating this distribution after Gauss. Around the end of 19th century, mathematicians started using the word ‘normal’ as an adjective for this distribution to reflect the fact that this distribution is typical, common and normal. Hence the terminology ‘normal distribution’ became popular for this distribution.
The bell shaped curve of normal distribution has several properties. The curve concentrates in the centre at the mean value of the data and decreases on either side. The pattern of decrease is similar in both directions and therefore the bell shaped curve is symmetric around its mean value. The bell shaped curve of normal distribution can be described using a mathematical expression that includes the mean and spread of the data.
The normal distribution is one of the important probability distributions in the field of statistics. Many methodologies, concepts and theories of statistics are based on the properties of normal distribution and the assumption of normal distribution of the data.
The normal distribution is ubiquitous in many branches of natural and social sciences. Scientists use the normal distribution for modelling of complex system as this is the simplest mathematical expression that nicely encapsulates a complex process. Many discoveries in sciences are based on hypothesis testing which uses the properties of the normal distribution extensively.
The normal distribution is considered the most prominent probability distribution in statistics. Normal distribution is encountered in biological, medical, physical, chemical, ecological, environmental and many other branches of natural and social sciences.
Data that are normally distributed is represented by a symmetric bell shaped curve where the centre of the curve is represented by the mean of the data.
Mathematicians Carl Friedrich Gauss and Pierre-Simon Laplace contributed significantly to the description of normal distribution around 19th century. That is the reason that the normal distribution is also called as Gauss-Laplacian distribution or simply as Gaussian distribution.