The Historical Evolution Of The Normal Distribution Entering Into Statistics

Due to its universality, Normal Distribution is the most important continuous distribution in Probability Theory. At the same time it is the cornerstone of the Statistics. So its proposal and application has special dual theoretical backgrounds and great value.From a historical perspective, there are three stages from its coming out to being a probability model of analyzing statistical data: in 1730s, De Moivre initially found the normal curve when he calculated an approximation of a probability, but for certain reasons it didn't become a probability distribution describing random phenomena; in1809, while studying the theory of error, Gauss firstly proposed it in form of the distribution and caused people's attention and extensive research, but people then thought that the observed data is compatible with the statistical data, so its applied scope was limited to the field of error, such as astronomy, geodesy, etc; entering the middle of 19th century, the work of Quetelet in the social sphere and Galton's research in the field of biology made the distribution expand to many natural and social science fields rapidly, and eventually it entered the Statistics and became the basis and the blasting fuses of a series of core theories.According to time sequence and based on the characters, this thesis consists of four parts: the proposal of the Normal Curve in Probability Theory(from the mid-17th century to the mid-18th century); the renascence of the Normal Distribution from the Theory of Error (from the mid-18th century to the mid-19th century); the entrance into the Recently Modern Statistics (from the mid-19th century to the late ); and the impact on the Modern Statistics (from the end of the 19th century to the 1930s ). According to the development backgrounds of different stages, this thesis gives an elaborate analysis and a summary on the evolution processes and the important work of the representative characters. Synchronously, it clarifies the interaction between the distribution and its related theories in different stages and underlines its sinuosity from generation to mature, the delicacy of the progress pushed by technique innovation and concept change and the general regular from penetration to blend, expecting to have some help on the modern historical research and education.