8/23/21 Chapter 1 & Background
● Population - All variables
○ Sample - Subset of population
● Population Variable - Attribute that has a value for each individual in the
population
○ A Population Variable in a Population “students” could be score or grade or
tests etc.
● Categorical variables (factor) place a case into one of several groups or categories
○ Examples of categorical variables in a “students” population could be grades
or opt-out etc.
○ Political preference is another example of a categorical variable
● Quantitative variables take numerical values QUANTITATIVE = NUMBERS
○ Examples of quantitative variables in a “students” population could be tests
or ID
○ Can be discrete or continuous
○ Number of siblings is another example of a categorical variable
● Discrete quantitative variables are a countable set of values
● Continuous quantitative variables are data that can take on any values within some
interval
○ Height of men on a professional basketball team are both quantitative and
continuous
---------------------------------------------------------------------------------------------------------------● A set is a collection of objects
○ Call S a set
● Elements are the items that are in a set
○ Call x an element in S, or x ∈ S
● We typically denote a set by capital letters of the English alphabet
○ Ei = E1, E2, E3…
○ E1 = {knife, spoon, fork}, E2 = {2,4,6,8}
○ The set E2 could also be written as E2 = {x|x are even integers between 0 and
10}
● The sample space of a random phenomenon is the set of all possible outcomes. Ω is
used to denote sample space.
○ Ω is all outcomes and events
● A venn diagram is a good tool for showing the relationships between sets