Section 1.1-1.2 - STT 351 Prob & Statistics for...

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STT 351 Instructor Details Name: Vellaisamy Palaniappan. (Address me as Vellai or Samy) Ph.D: IIT Kanpur, India. Profession : Professor at IIT Bombay, India At Present : Visiting MSU for 2 Semesters Papers Published : About 35 papers Countries visited : Japan, Canada, Germany, USA. 1
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STT 351- 4 1.1 Introduction Why statistics? (i) It is the science that helps to understand many phenomena which occur in your field of Engg. or Science. (ii) It is the scientific way that helps to make intelligent judgements / decisions in the presence of uncertainity and variation. We start with two examples. 2
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Example1: Emission levels of a vehicle: HC (gm/mile): 12.8 18.3 32.2 32.5 CO (gm/mile): 118 149 232 236 What is the CO level? Difficult to make a statement, as there is a high variation. Example2 : Marks of two students in 4 tests: S1: 25 38 42 39 S2: 85 62 78 59 Question: Who is doing better? Any difficulty in answering? No need for Statistical Analysis . 3
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What is statistics? (i) One word definition : (a) Economics : Money (b) Philosophy: Why (c) Statistics: Variation (ii) Layman definition: Information/summary of data. (iii) Formal Definition: Statistics deals with techniques to deal with or how to (a) obtain information /data (sample) (b) analyze scientifically the data (c) draw valid conclusions / inference (iv) as a branch of math, deals with analytical techniques to analyze the data to infer about the population. 4
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Population : The set of all well-defined objects/elements (of interest) which are under investigation. Example 1 : The students studying Engineering at MSU Example 2 : The population of East Lansing If we can collect information on all the elements in the population, we call it “Census”. Most often it is impossible; Sample : A subset of the population, which is selected for obtaining information. Eg. We may select 10 students from each discipline 5
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Often, we are interested in certain characteristics of the population (number of flaws in a piece of cloth; thickness of a capsule wall, monthly income of an individual etc). A characteristic may be (i) Categorical (belongs to one of the categories) A gender of a student (male/female); quality of a product (excellent / good / bad) (ii) Numerical (measured in real value) For example, (a) heights of students (b) values of a stock Types of Variables A variable is any characteristic which changes over the objects in the population. It is denoted by x,y,z (or by X,Y,Z) . The variables ‘x’ may be categorical ( called categorical variable) or numerical/quantitative (called numerical variable). 6
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Types of data (i) The data x 1 …… x n on a categorical variable x is called categorical data. (ii)
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Section 1.1-1.2 - STT 351 Prob & Statistics for...

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