Types of Variables

In studying statistics, we always deal with different data or our raw materials for investigations. In order to have the right tool of analysis for them, we must first know what type of variable we are considering. A variable is the characteristic about each individual element of a population or sample. Understanding the nature of variables will help us have better analysis of our data.

There are two kinds of variable. Here is a brief summary of these variables and their descriptions:

1. Qualitative, Attribute, or Categorical Variable – a variable that categorizes or describes an element of a population

- classified according to some criterion

a. Nominal Variable – a qualitative variable that categorizes (or describes, or names) an element of a population

b. Ordinal Variable – a qualitative variable that incorporates an ordered position, or ranking

2. Quantitative, or Numerical Variable – a variable that quantifies an element of a population

- are counts or measurement

a. Discrete Variable – a quantitative variable that can assume a countable number (also known as counting numbers or integers) of values, meaning, there is a gap between any two values

b. Continuous Variable – a quantitative variable that can assume an uncountable number (numbers with decimal points) of values, meaning, it can assume any value along a line interval

Examples:

1. X (Citizenship), X = American, English, Chinese, Filipino, Arabian, Japanese 
2. Y(Number of rooms), Y=1,2,3… 
3. Z(Value of house), o<z< infinity 
4. H(Health), H=poor, fair, good, excellent 
5. A(Number of hospital admissions), A=0,1,2,3,… 
6. V(Age of last birthday), V= 0,1,2,3,… 
7. W(True age,) O<W<infinity 
8. G(Gender), G = Male, Female

Exercises:

Identify the following as attribute (qualitative) or numerical (quantitative) variable, and then further as nominal, ordinal, discrete, or continuous variable.

1. The length of time until a pain reliever begins to work. 
2. The residence hall for each student in a statistics class.
3. The temperature in Barrow, Alaska at 12:00 pm on any given day.
4. The number of staples in a stapler.
5. Whether or not a 6-volt lantern battery is defective.
6. The pH level of the water in a swimming pool.
7. The number of colors in a statistics book.
8. The weight of a lead pencil.
9. The number of chocolate chips in a cookie.
10. The amount of gasoline pumped by the next 10 customers at the local Shell Station.
11. The color of the baseball cap worn by each of 20 students.
12. The type of book taken out of the library by an adult.
13. The make of automobile driven by each faculty member.
14. The number of files on a computer’s hard disk. 
15. The brand of refrigerator in a home.