Variables

A variable is a characteristic of a person or thing that can be recorded as a number or a category.

The people or things being observed are called observational units.

A characteristic is a variable when its value can differ from one observational unit to another.

1. Hair Color

For every student in a class, record the student’s hair color.

Observation	Hair color
Student 1	Brown
Student 2	Red
Student 3	Green
Student 4	Brown
etc.

1. Hair Color

For every student in a class, record the student’s hair color.

Question	Answer
Observational units	?
Characteristic recorded	?
Can the value differ from student to student?	?
Is it a variable?	?

1. Hair Color

For every student in a class, record the student’s hair color.

Question	Answer
Observational units	Students in the class
Characteristic recorded	Hair color
Can the value differ from student to student?	Yes
Is it a variable?	Yes

Hair color is a variable because different students can have different hair colors.

2. Instructor’s Age

For every student in a class, record the age of the instructor. The class has one instructor who is 33 years old.

Observation	Instructor’s age
Student 1	33
Student 2	33
Student 3	33
Student 4	33
etc.

2. Instructor’s Age

For every student in a class, record the age of the instructor.

Question	Answer
Observational units	?
Characteristic recorded	?
Can the value differ from student to student?	?
Is it a variable?	?

2. Instructor’s Age

For every student in a class, record the age of the instructor.

Question	Answer
Observational units	Students in the class
Characteristic recorded	Their instructor’s age
Can the value differ from student to student?	No
Is it a variable?	No

The value does not vary because every student has the same instructor.

3. Student Height

For every student in a class, record the student’s height in centimeters.

Observation	Height (cm)
Student 1	177
Student 2	162
Student 3	159
Student 4	168
etc.

3. Student Height

For every student in a class, record the student’s height in centimeters.

Question	Answer
Observational units	?
Characteristic recorded	?
Can the value differ from student to student?	?
Is it a variable?	?

3. Student Height

For every student in a class, record the student’s height in centimeters.

Question	Answer
Observational units	Students in the class
Characteristic recorded	Height in centimeters
Can the value differ from student to student?	Yes
Is it a variable?	Yes

Height is a variable because different students can have different heights.

4. Height of the Shortest Student

The shortest student in a class is 159 centimeters tall. For every student, record the height of the shortest student in the class.

Observation	Height of shortest student (cm)
Student 1	159
Student 2	159
Student 3	159
Student 4	159
etc.

4. Height of the Shortest Student

For every student, record the height of the shortest student in the class.

Question	Answer
Observational units	?
Characteristic recorded	?
Can the value differ from student to student?	?
Is it a variable?	?

4. Height of the Shortest Student

For every student, record the height of the shortest student in the class.

Question	Answer
Observational units	Students in the class
Characteristic recorded	Height of the class’s shortest student
Can the value differ from student to student?	No
Is it a variable?	No

This height summarizes the whole class. It does not vary from student to student.

5. ZIP Code

For every student in a class, record the ZIP code of the student’s hometown.

Observation	ZIP code
Student 1	10001
Student 2	08619
Student 3	90210
Student 4	11211
etc.

5. ZIP Code

For every student in a class, record the ZIP code of the student’s hometown.

Question	Answer
Observational units	?
Characteristic recorded	?
Can the value differ from student to student?	?
Is it a variable?	?

5. ZIP Code

For every student in a class, record the ZIP code of the student’s hometown.

Question	Answer
Observational units	Students in the class
Characteristic recorded	Hometown ZIP code
Can the value differ from student to student?	Yes
Is it a variable?	Yes

ZIP code is a variable. Although ZIP codes use digits, the digits identify categories rather than amounts.

Is It a Variable?

First identify the observational units.

Then identify the characteristic recorded for each observational unit.

Ask whether the value can differ from one observational unit to another.

If every observational unit must have the same value, the characteristic is not a variable for those units.