# 1.1-1.2 - STT 430 1.1 Introduction Why statistics? (i) It...

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STT 430 1.1 Introduction Why statistics? (i) It is the science that helps to understand many phenomena which occur in 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. 1

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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? 2
Any difficulty in answering? No need for Statistical Analysis . 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 3

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(iv) as a branch of math, deals with analytical techniques to analyze the data to infer about the population. 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; 4
Sample : A subset of the population, which is selected for obtaining information. Eg. We may select 10 students from each discipline 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 5

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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). Types of data (i) The data x 1 …… x n on a categorical variable x is called categorical data. (ii) The data x 1 …… x n on a numerical variable x is called quantitative data. Suppose we measure height = x, and weight = y on n- individuals, (x 1 , y 1 ), …… (x n , y n ). Then we have bivariate data. Similarly, multivariate data. Branches of Statistics (i) Descriptive Statistics : Deals with summarizing & describing important feature (such as mean, 6
median, standard deviation) of data (tabulating or graphical methods) (ii) Inferential Statistics : Deals with techniques for drawing inferences (generalizing to population) and predictions about the population, based on the information obtained from the sample. 1.2

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## This note was uploaded on 07/25/2008 for the course STT 430 taught by Professor Nane during the Spring '08 term at Michigan State University.

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1.1-1.2 - STT 430 1.1 Introduction Why statistics? (i) It...

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