Chapter 1: Introduction to Statistics PDF

Chapter 1 Not For Distribution Outside the Purview of Carleton University What’s meant by statistics? Statistics is a branch of mathematics that has applications in almost every facet of our daily life. Statistical methods provide powerful tools to collect, analyze, summarize and interpret data to...

Chapter 1 Not For Distribution Outside the Purview of Carleton University What’s meant by statistics? Statistics is a branch of mathematics that has applications in almost every facet of our daily life. Statistical methods provide powerful tools to collect, analyze, summarize and interpret data to reach informed decisions. Descriptive Statistics: is the science of summarizing and describing the important characteristics of a set of data. Inferential Statistics: is the science of using information obtained from a sample to infer about the characteristics of a population of interest. Populations and samples  A population is a set of the entire collection of units Population (individuals, objects).  A sample is a subset of the population selected in some Sample prescribed manner. A variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration. An experimental unit is the individual or object on which a variable is measured. A single measurement or data value is obtained when a variable is actually measured on an experimental unit.  Exercise 1 A set of five students is selected from all undergraduates at a large Canadian university and the data obtained is as shown in the following table: Student GPA Gender Major Credits 1 6.0 F Psychology 16 2 6.9 F Mathematics 15 3 8.7 M English 17 4 8.1 M English 15 5 7.8 F Business 14  Identify the population.  Identify the sample.  Identify the experimental unit.  Identify the measurement(s). Types of Data  Univariate data are obtained when a single variable is measured on a single experimental unit.  Bivariate data are obtained when two variables are measured on a single experimental unit.  Multivariate data are obtained when more than two variables are measured. Types of Variables Variables can be either qualitative or quantitative  Qualitative variables(Categorical) measure a quality or characteristic on each experimental unit. Measurements of qualitative variables belong to one of several categories.  Examples: ▪ Political affiliation: Liberals, Conservatives, NDP, Green, Independent ▪ The colour of a car ▪ The size of T-shirts: XS, S, M, L, XL ▪ Racers classified as coming in 1st, 2nd, 3rd, etc. Types of Variables  Quantitative variables measure a numerical quantity or amount on each experiment unit.  Examples: ▪ x= Prime interest rate ▪ x= A person’s weight ▪ x= Volume of orange juice in a glass ▪ x= The amount of rain in a specific day in Ottawa Quantitative variables can assume either continuous or discrete values. Types of Variables  Discrete variables can assume only a finite or countable number of values; x=0,1,2,3,.....  Continuous variables can assume the infinitely many values corresponding to the points on a line interval; 0