1. STATISTICS - The science of
collecting, describing, and interpreting data, to:
study the variation within a population
make predictions about the population
make conclusions about the population

2. POPULATION
Any collection of individuals, such as people, animals,
plants, products, etc.
SAMPLE
Any subset of a population. We often use very small
samples (relative to the population) to make assumptions
about the population.
VARIABLE
Any piece of information associated with an individual.
By data we mean a set of one or more variables taken from a population or sample.
CENSUS
A survey of an entire population. As this is often
difficult or impossible to obtain, we usually resort to a
sample survey.

3. QUANTITATIVE VARIABLES
Quantitative, or numerical, variables are variables that it
makes sense to “do math with”. Ask yourself if the
data can be averaged.
EXAMPLES:
height, weight, SAT scores, etc.
often we “quantify” information that seems non-numerical:
example:
strongly disagree = 0 disagree = 1
agree = strongly agree = 3

4. QUALITATIVE VARIABLES
Qualitative, or categorical variables are any variable
that can’t be quantified.
EXAMPLES:
RACE AND GENDER
EYE COLOR, PLACE OF BIRTH, ASTROLOGICAL SIGN
ZIP CODE, SOCIAL SRECURITY NUMBER, etc.
If we can’t do math with it, it’s not really quantitative
even if it has a numerical value.

5. CASE STUDY: Dr. Mellinger’s zip codes
I’ve lived in 4 states, with primary zip codes: PA
17543 DE
19716 IL
60302 VA
22401
The average of these 5 numbers is: 5
= = 29990 4
This isn’t even a valid zip code.
In this case, the “average” has no meaning.

6. Any time you find yourself confused by a problem
or statement, it can be useful to break the situation
down by asking 4 simple questions:
What are the individuals?
What is the population?
What is the variable of interest?
Is the variable quantitative or qualitative?
DON’T assume that a variable is quantitative simply
because there are numbers thrown around.

7. CASE STUDY:
“This is one of the largest classes I have ever taught.”
INDIVIDUALS:
POPULATION:
VARIABLE:
TYPE:
CLASSES
ALL CLASSES I HAVE TAUGHT
NUMBER OF STUDENTS
QUANTITATIVE

8. CASE STUDY:
“About 40% of the students in this class are freshmen.”
INDIVIDUALS:
POPULATION:
VARIABLE:
TYPE:
STUDENTS
ALL STUDENTS IN THIS CLASS
YEAR IN SCHOOL
QUALITATIVE
Again, don’t assume that a variable is quantitative simply
because there are numbers thrown around. Typically the
first thing we do with variables that aren’t quantitative is
count the number of individuals in each category.