With the changes of society, statistics have been inseparable from people's lives, and life is inseparable from statistics. Because statistics has been pushed to students before living in mathematics courses, in the modern society based on information and technology, people are faced with more opportunities and choices, and often need to make reasonable decisions based on a large number of unorganized data under uncertain circumstances. The following are some applications of statistics and probability in life: Example 1: Hardy is a famous mathematician in Britain. He respects the purity and beauty of mathematics and thinks that mathematics is a permanent work of art. He never talks about the application of mathematics. He wrote in the book: None of my discoveries can bring the slightest change to the comfort of the world ... Their work (referring to some mathematicians) is as useless as mine. But he didn't expect that a short article he published in 1908 had an important application in genetics. For example, a certain genetic disease (such as color blindness) will lead to more and more patients in a group because of inheritance from generation to generation? At the beginning of the 20th century, some biologists thought it was true. If so, it will certainly spread to future generations, and everyone will become a patient. Hardy pointed out that this statement was wrong with simple probability operation. He proved that the distribution of patients is stable and does not change with time. Example 2: An American TV manufacturing company was acquired by the Japanese, and the rejection rate of this company was high. After the Japanese applied mathematical statistics analysis, the rejection rate dropped to 2%. Example 3: AT&T Company uses mathematical statistics to improve the automatic assembly line, which is composed of several bodies, and its productivity is surprisingly low, but people can't find the reason. Mathematical statistics first collected data to determine the failure mode, and soon found that the crux of the problem was that the size of the plastic parts used in the production line changed too much, these plastic parts were too bent, and the solder joints of the metal parts were too thick, which led to the blocking of the machine operation. After one year's improvement, the productivity increased by 12 1%, the working hours decreased by 6 1%, and the product qualification rate increased from 90% to 98%. Ex. 4: It has become an essential application tool in quality control, forecasting and management (including capital investment, product production and sales, and personnel organization). Mathematicians in China have made a lot of statistical predictions on weather, typhoons, earthquakes, pests and diseases, fish schools and waves. The average error between the continuous 1 1 year predicted output of Chinese Academy of Sciences and the actual output is only 1%. In primary school, students should be trained to collect and process data and make appropriate choices and judgments based on the data. It is precisely because of the importance of statistics that "statistical concept" is regarded as one of the important goals of compulsory education mathematics curriculum for the first time in China. First of all, briefly introduce the development of statistics. Statistics is a very old science. It is generally believed that its theoretical research began in Aristotle's time in ancient Greece and has a history of more than 2300 years. It originated from the study of social and economic problems, and it is still the basic method for us to study social and economic problems. In the development process of more than two thousand years, statistics has experienced at least three stages of development: polis politics, political arithmetic and statistical analysis science. Probability theory is the theoretical basis of mathematical statistics. Today, statistics has developed into an independent discipline, but it has not yet reached unity. As early as 1869, when discussing the definition of statistics, it was said that there were more than 180 kinds. There is a view in our country that statistics is a methodological science to study a large number of data, or, as the Encyclopedia Britannica said, it is "the science and art of collecting and analyzing data". Historical interpretation: Statistics originated from the quantitative interpretation and research of social and economic problems. It is a tool to help decision-making and assist management. As I said just now, probability theory, the theoretical basis of modern statistics, began with the study of gambling opportunities:17th century, there was a famous gambler in France, and his name was Moeller. One day, he gambled with the guards to throw a sieve, and both of them put 30 gold coins. It is agreed that Moeller will win 60 gold coins by throwing six points three times first, and the guard will win 60 gold coins by throwing four points three times first. When Moeller threw 6 points twice and the bodyguard shot 1 4 points, something unexpected happened. The bodyguard officer was informed that he must go back to accompany the king to meet the foreign guests at once. Gambling can't continue, but how to distribute the bets made by two people? Moeller thinks he should get all three quarters, and the bodyguard thinks he should get all one third. They argued endlessly, and finally Moeller wrote to ask Pascal, a famous French mathematician. Pascal found it very interesting, so he wrote to Fermat on July 29th, 1654, and had an exchange and discussion with Fermat, which finally laid a branch of mathematics-probability theory. With the long-term research, the theoretical framework of probability theory has gradually formed. Modern statistical methods have a solid theoretical foundation.