1.3 Exploring Categories of Data, Levels of Measurement Practice

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 what type of data?

(1) quantitative discrete data

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

(1) quantitative discrete 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 6.2, 7, 6.8, 9.1, 4.3. Notice that backpacks carrying three books can have different weights. What type of data is this?

(1) quantitative continuous data

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

(1) quantitative continuous data

You go to the supermarket and purchase three cans of soup (19 ounces tomato bisque, 14.1 ounces lentil, and 19 ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies). Name data sets that are quantitative discrete, quantitative continuous, and qualitative.

The following list of materials was purchased by a purchase manager in a company:
• Two types of nails (2 kg box nails, 3 kg roofing nails)
• One type of oil (4 L machine oil)
• Four types of screws (3 kg wood screws, 5 kg machine screws, 1 kg set screws, 2 kg socket screws)

Name data sets that are quantitative discrete, quantitative continuous, and qualitative.

Qualitative: Type of nails, oil, screws
Discrete: Number of nails, number of type of oil, number of screws (1 nails, 1 type of oil, 4 types of screws)
Continuous: Weights of each (2kg nails, 3kg roofing nails, 4L machine oil, 3kg wood screws, 5kg machine screws, 1kg set screws, 2kg socket screws)

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. What type of data is this?

(1) Qualitative data

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?

(1) Qualitative data

This pie chart shows the students in each year, which is qualitative (or categorical) data.