6 1. ONE-VARIABLE STATI STICS: BASICS
would essentially be the collection of all the names on all class rosters of courses in t he last
five years at all US 4-year colleges and universities.
When doing an actual scientific study, we are usually not interested so much in the
individuals themselves, but rather in
DEFINITION 1.1.5. A variable in a statistical study is the answer o f a question the
researcher is aski ng about each individual. There are two types:
• A categorical variable is one whose values have a finite number of possibilities.
• A quantitative variable is one whose values are numbers (so, potentially an infi-
nite number of possibilities).
The variable is something which (as the name says) varies, in the s ense that it can have
a different value for each individual in the population (although that is not necessary).
EXAMPLE 1.1.6. In E xample 1.1.2, the variable most likely would be who they voted
for, a categorical variable with on ly possible values “Mickey Mouse” or “Daffy Du ck” (or
whoever the n ames on the bal lot were).
EXAMPLE 1.1.7. In Example 1.1.3, the variable most likely would be what f a ce of the
coin was facing up after t he flip , a categorical variable with values “heads” and “tails.”
EXAMPLE 1.1.8. There are several variables we might use i n Example 1.1.4. One
might be ho w many homework p roblems did the s tudent do in that course. Another could
be how many hours total did the student spend doing homework over that whole semester,
for that course. Both of those would be quantitative variables.
A categorical variable for th e same population would be what lett er grade did the stu -
dent get in the course, which has poss ible values A, A-, B+, . . . , D-, F.
In many [most?] interesting studi es, the po pulation is too large for it to be practical to
go observe the values of some interesting variable. Sometimes it is not just im practical, but
actually impossible – think of the example we gave of all the flips of the coin, even in the
ones in the future. So instead, we often work with
DEFINITION 1.1 . 9. A sample is a s ubset of a population under stu dy.
Often we use the variable N to indicate the size of a whole pop u lation and the variable
n for the size of a sam ple; as we have sai d, usually n < N.
Later we shall discuss how to pick a good sample, and how much we can learn about
a population from looking at the values of a variable of interest only for the individuals in
a sample. For the rest of this chapter, however, let’s just consider what to do with these
sample values.
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