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Quantitative Methods
QMS 102
Sheila Rosenberg

Alyssa Soubliere Ryerson University September 9, 2013 QMS102 Lecture One Notes Date Types, Measurement Scales, Stem-and-Leaf Plot Chapter1-3Notes Data and Statistics:  Data are information or facts in a form that can be stored and used  Statistics is a branch of applied mathematics used for collecting, organizing, presenting, analyzing, and interpreting data  Statistics is divided into two categories: o Descriptive Statistics focuses on collecting, organizing, presenting, and analyzing data o Inferential Statistics uses data that have been collected from a smaller group to infer (draw or conclude) something about a larger group Data Collection:  Data collection is the process of gathering information using questionnaires/surveys, interviews, experiments, etc.  Data may be collected from two sources: o Primary Data- the raw or original data collected directly from respondents using surveys and observations o Secondary Data- collected by another source (Stats Canada, or Government Data) Basic Terminology:  Population is a group that includes all objects/subjects in your study. Population Size is the number of subjects in that population. The population size is denoted as N.  Census is a set of data that includes all members of a population  Sample is a subset of a population. Sample Size is the number of object/subjects in a sample. The sample size is denoted by n.  Variable is a feature, number, or quantity that can be measured or counted. Each variable has a name and a value (If the survey question is “Did you bring your textbook today?” The answers would be yes or no, meaning the variable would be textbook). Example One: refer to Table 1.1 of Business Statistics Textbook What can we say about this survey?  The population is a group of students. We aren’t told the population size.  The sample size is 12. This sample was randomly selected.  There were 5 questions. The possible answers were {Yes, No}, an integer, a real number, way of transportation, etc.  The variable in Q1 can be “textbook”, the variables can be {Yes & No}. Alyssa Soubliere Ryerson University September 9, 2013 QMS102 Lecture One Notes Date Types, Measurement Scales, Stem-and-Leaf Plot  The variable in Q2 can be “number of hours” the possible values of the variable are real numbers in the interval of [0, 168]  The variable in Q3 can be “number of classes” the possible values of the variable are positive integers {0, 1, 2, 3, 4, 5, 6, 7}  The variable in Q4 can be “class year”, the possible values of the variables are {Freshman, Sophomore, Junior, and Senior}. One could have assigned the values of this variable to be positive integers {1, 2, 3, and 4}. Either way an important feature is that there is a natural order rd th of the values (Junior is lower than Senior in the hierarchy or the 3 year is lower than the 4 year student in the hierarchy).  The variable for Q5 can be “way of transportation”, the possible values of the variable are {Walk, Drive, Public Transport, Car Pool}. In this case there is no natural order of the values. Variable Types: Variables are classified into types according to the ways they can be measured or described  Numeric Variables o The values of Numeric Variables are numbers that arise from measuring ‘how many’ or ‘how much’. Hence we call them quantitative variables.  Categorical Variables o The variables of categorical variables are descriptions of a ‘feature’ or ‘characteristic’ of an item, like ‘what type’ or ‘which category’. Hence, we call them qualitative variables ad they are non-numeric in nature. Numeric variables can be either discrete or continuous  Discrete variables have numerical values that arise from a counting process. So, the value of a discrete variable is an integer. E.g. the number of students in different sections of this course, the number of cafeterias on campus which are measured in whole units (1, 2, 3, 4)  Continuous variables have numerical values that arise from a measuring process. So, the value of a continuous variable is a real number. It can take any value or interval. E.g. age, weight, time. Categorical variables can be either nominal or ordinal  Nominal variables have no particular or ranking in their category, i.e. they take values we cannot organize in a logical way. Examples can include eye colour, religion, car brand, postal cod
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