Data Types and Variable Types

Data Type = Variable Type

Sometimes we talk about data types, and sometimes about variable types. They’re the same thing. For instance, “weight of a machine part” is a continuous variable, and 61.1 g, 61.4 g, 60.4 g, 61.0 g, and 60.7 g are continuous data.

Quantitative or Qualitative?

There are two main types of data, quantitative (a/k/a numeric) and qualitative (a/k/a attribute or non-numeric).

Be careful with variables that look numeric but aren’t. For instance, your telephone area code is three digits. But an “average area code” would be nonsense, so area code is a qualitative variable, not quantitative. Can you think of another example of a variable that is numeric at first sight but is really non-numeric?

Types of Qualitative Data

Qualitative or attribute variables divide into two types. You should know them, although your book does not tell you. and when identifying a data type you should use the more specific term.

• Binomial variables have only two values. Examples are gender, citizenship in a given country, and getting a passing grade in MATH200. All of these are yes/no questions.
• Categorical variables are qualitative variables with more than two possible answers. Examples are marital status (you can be single, married, widowed, or divorced), country of origin, political party affiliation, religious affiliation, choice of major.

There are some doubtful cases. For example, what about opinion polls? “Are you for or against X?” looks binomial. But look deeper. Does the poll allow for “unsure” or “no opinion”? If so, the variable is categorical; but if only “for” and “against” are possible responses then it is binomial.

Types of Quantitative Data

Quantitative or numeric variables divide into two subtypes, as indicated on page 7. Again, when identifying data types use the more specific terms.

• Discrete variables have only a small to moderate number of possible values and almost always answer “how many?” questions. Examples: number of children in a family, number of times a person was married, number of years of college completed.
• Continuous variables can take any value, or any value within a specified range: you can subdivide the values. A “how much” question is a continuous variable. Examples: height, weight of bags of sugar, diameter of an apple.

There are some doubtful cases, such as salary and age.

It’s true that your salary can be only a whole number of pennies. But there are a great many possible values, and the distance between the possible values is quite small, so we say that salary is a continuous variable. Besides, you don’t ask “how many pennies do you make?” but rather “how much do you make?”

What about age? Well, age at last birthday is clearly discrete since it can be only a whole number: “how many years old were you at your last birthday?” But age now, including years and months and days and fractions of days, would be continuous, again because you can subdivide it as finely as desired.

Summary Statements

When you see a summary statement, you have to do a little mental detective work to figure out the data type. Always ask yourself, what was the original measurement taken or question asked?

Example: “The average salary at our corporation is $22,471.” The original measurement was the salary of each individual, so this is continuous data.

Example: “The average American family has 1.7 children.” Don’t let “1.7” fool you into identifying this as a continuous variable! What was the original question or measurement? “How many children are there in your family?” That’s discrete data.

Example: “Four out of five dentists surveyed recommend Trident sugarless gum for their patients who chew gum.” Yes, there are numbers in the summary statement, but the original question asked of each dentist was “Do you recommend Trident?” That is a yes/no question, so the data type is binomial.

What’s New

• 26 Aug 2009: add a table compating qualitative and quantitative data
• 5 Jun 2009: new document