AP Statistics Tutorial: Variables
In statistics, a variable has two defining characteristics:
- A variable is an attribute that describes a person, place, thing,
or idea.
- The value of the variable can "vary" from one entity to another.
For example, a person's hair color is a potential variable,
which could have the value of "blond" for one person and
"brunette" for another.
Qualitative vs. Quantitative Variables
Variables can be classified as qualitative (aka, categorical)
or quantitative (aka, numeric).
- Qualitative. Qualitative variables take on values that are names
or labels. The color of a ball (e.g., red, green, blue) or the
breed of a dog (e.g., collie, shepherd, terrier) would be examples
of qualitative or categorical variables.
- Quantitative. Quantitative variables are numeric. They represent a
measurable quantity. For example, when we speak of the
population of a city, we are talking about the number of people
in the city - a measurable attribute of the city. Therefore,
population would be a quantitative variable.
In algebraic equations, quantitative variables are represented by symbols
(e.g., x, y, or z).
Discrete vs. Continuous Variables
Quantitative variables can be further classified as discrete
or continuous. If a variable can take on any value between
its minimum value and its maximum value, it is called a continuous variable;
otherwise, it is called a discrete variable.
Some examples will clarify the difference between discrete and
continouous variables.
- Suppose the fire department mandates that all fire fighters must weigh
between 150 and 250 pounds. The weight of a fire fighter would be an
example of a continuous variable; since a fire fighter's weight could
take on any value between 150 and 250 pounds.
- Suppose we flip a coin and count the number of heads. The number of heads
could be any integer value between 0 and plus infinity. However, it could
not be any number between 0 and plus infinity. We could not, for example,
get 2.3 heads. Therefore, the number of heads must be a discrete
variable.
Univariate vs. Bivariate Data
Statistical data are often classified according to the number of variables
being studied.
- Univariate data. When we conduct a study that looks at only
one variable,
we say that we are working with univariate data. Suppose, for example,
that we conducted a survey to estimate the average weight of high
school students. Since we are only working with one variable (weight), we
would be working with univariate data.
- Bivariate data. When we conduct a study that examines
the relationship between two variables, we are working with bivariate
data. Suppose we conducted a study to see if there were a relationship
between the height and weight of high school students. Since we are
working with two variables (height and weight), we would be working
with bivariate data.
Test Your Understanding of This Lesson
Problem 1
Which of the following statements are true?
I. All variables can be classified as quantitative or categorical variables.
II. Categorical variables can be continuous variables.
III. Quantitative variables can be discrete variables.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Solution
The correct answer is (E). All variables can be classified as quantitative or
categorical variables. Discrete variables are indeed a category of quantitative
variables. Categorical variables, however, are not numeric. Therefore, they
cannot be classified as continuous variables.
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