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

POPULATIONAny collection of individuals, such as people, animals,plants, products, etc.

SAMPLEAny subset of a population. We often use very small samples (relative to the population) to make assumptions about the population.

VARIABLEAny piece of information associated with an individual.By data we mean a set of one or more variables taken from a population or sample.

CENSUSA survey of an entire population. As this is often difficult or impossible to obtain, we usually resort to asample survey.

QUANTITATIVEQUANTITATIVEVARIABLESVARIABLES

Quantitative, or numerical, variables are variables that itmakes sense to “do math with”. Ask yourself if thedata can be averaged.EXAMPLES:

height, weight, SAT scores, etc.

often we “quantify” information that seems non-numerical: example:

strongly disagree = 0 disagree = 1 agree = 2 strongly agree = 3

QUALITATIVE QUALITATIVE VARIABLESVARIABLES

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 quantitativeeven if it has a numerical value.

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:

17543+19716+60302+22401 5

= 119962 = 29990 4

This isn’t even a valid zip code.

In this case, the “average” has no meaning.

Any time you find yourself confused by a problemor 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.

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

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 iscount the number of individuals in each category.