Quantitative versus Qualitative Data

Learning Outcomes

  • Determine if a give variable is quantitative or qualitative (categorical)
  • Determine if a given quantitative variable is discrete or continuous

Data may come from a population or from a sample. Small letters like [latex]x[/latex] or [latex]y[/latex] 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. Qualitative data are also often called categorical data. 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, or red. Blood type might be AB+, O-, or B+. Researchers often prefer to use quantitative data over qualitative data because it lends itself more easily to mathematical analysis. For example, it does not make sense to find an average hair color or blood type.

Quantitative data are always numbers. 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 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 values such as zero, one, two, or three.

Data that are not only made up of counting numbers, but that may include fractions, decimals, or irrational numbers, are called quantitative continuous data. Continuous data are often the results of measurements like lengths, weights, or times. A list of the lengths in minutes for all the phone calls that you make in a week, with numbers like [latex]2.4, 7.5, \mathrm{or} \ 11.0[/latex], would be quantitative continuous data.

Example

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 three books, one student carries four books, one student carries two books, and one student carries one book. The numbers of books (three, four, two, and one) are the quantitative discrete data.

Try It

The data are the number of machines in a gym. You sample five gyms. One gym has [latex]12[/latex] machines, one gym has [latex]15[/latex] machines, one gym has [latex]10[/latex] machines, one gym has [latex]22[/latex] machines, and the other gym has [latex]20[/latex] machines. What type of data is this?

Example

Data sample of quantitative continuous data
The data are the weights of backpacks with books in them. You sample the same five students. The weights (in pounds) of their backpacks are [latex]6.2[/latex], [latex]7[/latex], [latex]6.8[/latex], [latex]9.1[/latex], [latex]4.3[/latex]. Notice that backpacks carrying three books can have different weights. Weights are quantitative continuous data because weights are measured.

try it

The data are the areas of lawns in square feet. You sample five houses. The areas of the lawns are [latex]144[/latex] sq. feet, [latex]160[/latex] sq. feet, [latex]190[/latex] sq. feet, [latex]180[/latex] sq. feet, and [latex]210[/latex] sq. feet. What type of data is this?

Example

You go to the supermarket and purchase three cans of soup ([latex]19[/latex] ounces tomato bisque, [latex]14.1[/latex] ounces lentil, and [latex]19[/latex] ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts ([latex]16[/latex] ounces pistachio ice cream and [latex]32[/latex] ounces chocolate chip cookies).

Name data sets that are quantitative discrete, quantitative continuous, and qualitative. Also try to identify additional data sets in this example.

Example

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.

try it

The data are the colors of houses. You sample five houses. The colors of the houses are white, yellow, white, red, and white. What type of data is this?

Example

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. the distance it is from your home to the nearest grocery store
  4. the number of classes you take per school year
  5. the type of calculator you use
  6. weights of sumo wrestlers
  7. number of correct answers on a quiz
  8. IQ scores (this may cause some discussion)

try it

Determine the correct data type (quantitative or qualitative) for the number of cars in a parking lot. Indicate whether quantitative data are continuous or discrete.

Example

A statistics professor collects information about the classification of her students as freshmen, sophomores, juniors, or seniors. The data she collects are summarized in the pie chart Figure 1.3. What type of data does this graph show?

This is a pie chart showing the class classification of statistics students. The chart has 4 sections labeled Freshman, Sophomore, Junior, Senior. The largest section is Freshman, the second largest is Sophomore, the third largest is Junior, and the smallest is Senior.

Figure 1.

try it

The registrar at State University keeps records of the number of credit hours students complete each semester. The data he collects are summarized in the histogram. The class boundaries are [latex]10[/latex] to less than [latex]13[/latex], [latex]13[/latex] to less than [latex]16[/latex], [latex]16[/latex] to less than [latex]19[/latex], [latex]19[/latex] to less than [latex]22[/latex], and [latex]22[/latex] to less than [latex]25[/latex].

This histogram consists of 5 bars with the x-axis marked at intervals of 3 from 10 to 25, and the y-axis in increments of 100 from 0 to 800. The height of bars shows the number of students in each interval. Interval 10 to 13 is at 250, interval 13 to 16 is at 580, interval 16 to 19 is at 720, interval 19 to 22 is at 620, and interval 22 to 25 is at 250.

What type of data does this graph show?