b.lect2

# b.lect2 - Outline Random Variables and Statistical...

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Outline Random Variables and Statistical Populations Proportions, Averages, Variances and Percentiles Lecture 2 Chapter 1: Basic Statistical Concepts M. George Akritas M. George Akritas Lecture 2 Chapter 1: Basic Statistical Concepts

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Outline Random Variables and Statistical Populations Proportions, Averages, Variances and Percentiles Random Variables and Statistical Populations Proportions, Averages, Variances and Percentiles Proportions: Population- and Sample- Averages: Population- and Sample- Variance: Population- and Sample- Sample Percentiles M. George Akritas Lecture 2 Chapter 1: Basic Statistical Concepts
Outline Random Variables and Statistical Populations Proportions, Averages, Variances and Percentiles Variable = a Numerical Characteristic If the characteristic of interest can be measured expressed as a number, e.g. thermal expansion of a metal, hardness of cement, mercury concentration, or number of accidents it is are called quantitative . Examples of non-quantitative characteristics are gender, make of car, eye color, strength category, political affiliation. Such characteristics are called categorical or qualitative . Because statistical procedures are applied to numerical data sets, the categories in categorical characteristic are labeled with arbitrarily chosen numbers (i.e. ’male’= - 1, ’female’= +1). A characteristic expressed as a number is called a variable . M. George Akritas Lecture 2 Chapter 1: Basic Statistical Concepts

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Outline Random Variables and Statistical Populations Proportions, Averages, Variances and Percentiles Types of Variables I Qualitative variables are a particular kind of discrete variables. Quantitative variables can also be discrete. I All variables expressing counts, such as the number of earthquakes, the number of fish caught etc, are discrete. I Quantitative variables expressing measurements on a continuous scale are examples of continuous variables. I Measurements of length, strength, weight, or time to failure are examples of continuous variables. I When two or more characteristics are measured on each population unit, we have bivariate or multivariate variables. I Example of bivariate: Salary increase and productivity. I Example of multivariate: Age, income, education level. M. George Akritas Lecture 2 Chapter 1: Basic Statistical Concepts
Outline Random Variables and Statistical Populations Proportions, Averages, Variances and Percentiles Random Variables I When a unit is randomly sampled from a population, the value of its variable will be denoted by X (or Y, or Z, etc). I Because of the intrinsic variability, X is not known a-priori and thus it is called a random variable (r.v.). I The population from which a random variable is drawn is called the underlying population of the r.v. I The collection of of the variable values of all population units is called the statistical population .

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