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在实践中,我们常常只能从整体事物的一部分来观察和研究它的某些性质。现代化的工厂一天的产量是几万件甚至几十万件,要鉴定全部产品中每一件产品的品质是极其困难的。还有,如棉纱强力、电灯泡的寿命等检验,被检验产品将被毁损,那就更不可能全面检验。我们只能抽取产品中一部分来检验,从而推断整批产品的质量。在数理统计学里,我们把整批产品叫做一个总体,抽取出来的一个样本叫做子样。数理统计是用概率理论来研究总体与子样间之关系的科学。因此,数理统计学在产品检验,纺织试验,天气预报,工程设计等各个方面得到广泛的应用。下面就我们这次下工厂学习数理统计时,遇到的几个实用问题和数理统计的基本知识作一简要的介绍,错误的地方,希望同志们指正。
In practice, we can often observe and study some of its properties from only a part of the whole thing. The output of modern factories is tens of thousands or even hundreds of thousands of products a day. It is extremely difficult to identify the quality of each product in all products. Also, if the strength of cotton yarns, the life of electric bulbs, etc., are tested, the products being tested will be damaged, and it will be even less likely to be fully tested. We can only take part of the product to inspect, and infer the quality of the entire batch. In mathematical statistics, we call the entire batch of products a population, and a sample taken out is called a sub-sample. Mathematical statistics is the science of using probabilistic theory to study the relationship between population and subsamples. Therefore, mathematical statistics has been widely used in product inspection, textile testing, weather forecasting, and engineering design. The following is a brief introduction to the practical problems we encountered and the basic knowledge of mathematical statistics when we went to study the mathematical statistics at the factory. The wrong place, I hope comrades correct me.