lect1_st_2016.doc - LECTURE 1 Introduction to Statistics...

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L E C T U R E 1 Introduction to Statistics All life a person has to make decisions: in personal sphere (in which university or college to enter, with whom to communicate; how to study); in public (to attend evenings, theatres, meetings, assemblies, elections); in industrial (determining factors essentially influencing on productivity, quality of materials and etc.); in scientific (nominating and checking scientific hypotheses). Decision-making usually pursues one of the following purposes: forecasting a future state of a process (an object); controlling (i.e. how should to change certain parameters of an object in order that other parameters have taken on a desirable value); an explaining an internal structure of an object. Usually decision-making is preceded with an analysis of known data (on the basis of previous experience, common sense, intuition, and etc.). Aspiring to see and prove regularities in uncertain processes, the mankind has developed the whole arsenal of methods which refer to as mathematical statistics ( applied statistics or data analysis ). Mathematical statistics is a section of mathematics in which mathematical methods of ordering, processing and using statistical data for scientific and practical conclusions are studied. Abraham Wald (1902-1950) spoke that «mathematical statistics is theory of decision-making in conditions of uncertainty». In essence mathematical statistics gives a unique, mathematically proved apparatus for solving problems of control and forecasting at absence of obvious regularities (presence of randomness) in investigated processes. Two kinds of statistical observations are distinguished in practice: continuous when all objects of a set are studied, and not continuous, sampling when a part of objects is studied. An example of continuous observation is the population census covering all population of the country. A sampling observation is, for example, spent sociological investigations covering a part of the population of a country, district and etc. All set of objects (observations) subject to studying is said to be a parent population . A part of objects which is selected for direct studying from a parent population is said to be a sample population or a sample . Numbers of objects (observations) of a parent or sample population are said to be their volumes (sizes) . A parent population can have both finite and infinite volume. The essence of a sampling method is to make a judgment on properties of a parent population as a whole by some its part (by a sample). Advantages of sampling: It allows to save essentially expenses of resources (material, labor, time); It is uniquely possible in case of an infinite parent population or in case when the investigation is connected with destruction of observable objects (for example, investigation of durability of electric bulbs, limiting operating modes of devices, etc.); At the same expenses of resources one enables to conduct a deep research due to expanding a program of research; It allows to lower mistakes of registration, i.e. divergences between true and registered values of an
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