1.4 Types of Data
You have learned that statistics is the science of data and that data are obtained by measuring the values of one or more variables on the units in the sample (or population). All data (and hence the variables we measure) can be classified as one of two general types: quantitative data and qualitative data.
Quantitative data are data that are measured on a naturally occurring numerical scale.* The following are examples of quantitative data:
The temperature (in degrees Celsius) at which each piece in a sample of 20 pieces of heat-resistant plastic begins to melt
The current unemployment rate (measured as a percentage) in each of the 50 states
The scores of a sample of 150 law school applicants on the LSAT, a standardized law school entrance exam administered nationwide
The number of convicted murderers who receive the death penalty each year over a 10-year period
Quantitative data are measurements that are recorded on a naturally occurring numerical scale.
In contrast, qualitative data cannot be measured on a natural numerical scale; they can only be classified into categories.* (For this reason, this type of data is also called categorical data.) Examples of qualitative data include the following:
The political party affiliation (Democrat, Republican, or Independent) in a sample of 50 voters
The defective status (defective or not) of each of 100 computer chips manufactured by Intel
The size of a car (subcompact, compact, midsize, or full size) rented by each of a sample of 30 business travelers
A taste tester’s ranking (best, worst, etc.) of four brands of barbecue sauce for a panel of 10 testers
Often, we assign arbitrary numerical values to qualitative data for ease of computer entry and analysis. But these assigned numerical values are simply codes: They cannot be meaningfully added, subtracted, multiplied, or divided. For example, we might code Democrat Republican and Independent Similarly, a taste tester might rank the barbecue sauces from 1 (best) to 4 (worst). These are simply arbitrarily selected numerical codes for the categories and have no utility beyond that.
Qualitative (or categorical) data are measurements that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories.
Example 1.4 Data Types—Army Corps of Engineers Study of a Contaminated River
Problem
Chemical and manufacturing plants often discharge toxic-waste materials such as DDT into nearby rivers and streams. These toxins can adversely affect the plants and animals inhabiting the river and the riverbank. The U.S. Army Corps of Engineers conducted a study of fish in the Tennessee River (in Alabama) and its three tributary creeks: Flint Creek, Limestone Creek, and Spring Creek. A total of 144 fish were captured, and the following variables were measured for each:
River/creek where each fish was captured
Species (channel catfish, largemouth bass, or smallmouth buffalo fish)
Length (centimeters)
Weight (grams)
DDT concentration (parts per million)
(For future analyses, these data are saved in the FISHDDT file.) Classify each of the five variables measured as quantitative or qualitative.
Solution
The variables length, weight, and DDT concentration are quantitative because each is measured on a numerical scale: length in centimeters, weight in grams, and DDT in parts per million. In contrast, river/creek and species cannot be measured quantitatively: They can only be classified into categories (e.g., channel catfish, largemouth bass, and smallmouth buffalo fish for species). Consequently, data on river/creek and species are qualitative.
Look Ahead
It is essential that you understand whether the data you are interested in are quantitative or qualitative, since the statistical method appropriate for describing, reporting, and analyzing the data depends on the data type (quantitative or qualitative).
Now Work Exercise 1.12
We demonstrate many useful methods for analyzing quantitative and qualitative data in the remaining chapters of the text. But first, we discuss some important ideas on data collection in the next section.