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Quantitative Methods
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QMS 102
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Quantitative Methods

QMS 102

Sheila Rosenberg

Fall

Description

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
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