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Sampling and Data: Data

Module by: Barbara Illowsky, Susan Dean

Summary: This module introduces the concepts of qualitative data, quantitative continuous data, and quantitative discrete data as used in statistics. Sample problems are included. Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

Data may come from a population or from a sample. Small letters like x x or y y generally are used to represent data values. Most data can be put into the following categories:
  • Qualitative
  • Quantitative
Qualitative data are the result of categorizing or describing attributes of a population. Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. Qualitative data are generally described by words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, and red. Blood type might be AB+, O-, or B+. Qualitative data are not as widely used as quantitative data because many numerical techniques do not apply to the qualitative data. For example, it does not make sense to find an average hair color or blood type.
Quantitative data are always numbers and are usually the data of choice because there are many methods available for analyzing the data. Quantitative data are the result of counting or measuring attributes of a population. Amount of money, pulse rate, weight, number of people living in your town, and the number of students who take statistics are examples of quantitative data. Quantitative data may be either discrete or continuous.
All data that are the result of counting are called quantitative discrete data. These data take on only certain numerical values. If you count the number of phone calls you receive for each day of the week, you might get 0, 1, 2, 3, etc.
All data that are the result of measuring are quantitative continuous data assuming that we can measure accurately. Measuring angles in radians might result in the numbers π6 π6, π2π2 , 3π43π4 , etc. If you and your friends carry backpacks with books in them to school, the numbers of books in the backpacks are discrete data and the weights of the backpacks are continuous data.
Example 1: Data Sample of Quantitative Discrete Data 
The data are the number of books students carry in their backpacks. You sample five students. Two students carry 3 books, one student carries 4 books, one student carries 2 books, and one student carries 1 book. The numbers of books (3, 4, 2, and 1) are the quantitative discrete data.
Example 2: Data Sample of Quantitative Continuous Data 
The data are the weights of the backpacks with the books in it. You sample the same five students. The weights (in pounds) of their backpacks are 6.2, 7, 6.8, 9.1, 4.3. Notice that backpacks carrying three books can have different weights. Weights are quantitative continuous data because weights are measured.
Example 3: Data Sample of Qualitative Data 
The data are the colors of backpacks. Again, you sample the same five students. One student has a red backpack, two students have black backpacks, one student has a green backpack, and one student has a gray backpack. The colors red, black, black, green, and gray are qualitative data.
Note: You may collect data as numbers and report it categorically. For example, the quiz scores for each student are recorded throughout the term. At the end of the term, the quiz scores are reported as A, B, C, D, or F.
Example 4 
Problem 1
Work collaboratively to determine the correct data type (quantitative or qualitative). Indicate whether quantitative data are continuous or discrete. Hint: Data that are discrete often start with the words "the number of."
  1. The number of pairs of shoes you own.
  2. The type of car you drive.
  3. Where you go on vacation.
  4. The distance it is from your home to the nearest grocery store.
  5. The number of classes you take per school year.
  6. The tuition for your classes
  7. The type of calculator you use.
  8. Movie ratings.
  9. Political party preferences.
  10. Weight of sumo wrestlers.
  11. Amount of money (in dollars) won playing poker.
  12. Number of correct answers on a quiz.
  13. Peoples' attitudes toward the government.
  14. IQ scores. (This may cause some discussion.)
[ Click for Solution 1 ]
Solution 1
Items 1, 5, 11, and 12 are quantitative discrete; items 4, 6, 10, and 14 are quantitative continuous; and items 2, 3, 7, 8, 9, and 13 are qualitative.
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Glossary

Continuous RV:
A RV with continuous domain. Ex.: height of trees in the forest.
Data:
A set of observations (a set of possible outcomes). Most data can be put into two groups: qualitative (hair color, ethnic groups and many other attributes of population) and quantitative (distance traveled to college, number of children in a family, etc.). In its turn quantitative data can be separated into two subgroups: discrete and continuous. Roughly speaking, data is discrete if it is result of counting (a number of student of the given ethnic group in a class, a number of books on a shelf, etc.), and data is continuous if it is result of measuring (distance traveled, weight of luggage, etc.)
Discrete RV:
A RV that can assume only countable set of values. (Ex.’s.: (1). Face nominations of cubic die ={1,2,3,4,5,6}={1,2,3,4,5,6} size 12{ {}= lbrace 1,2,3,4,5,6 rbrace } {}, (2). a number of accidents on HW280 at Thanksgiving Holidays).
Qualitative Data:
See Data.
Quantitative:
See Data.

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