1.2 Data Basics
Types of Data
Data may come from a population or from a sample. Lowercase letters like x or y are generally used to represent data values. Most data falls into the following categories:
Qualitative or categorical data come in many forms. Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. Categorical data can generally be described with 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+.
Quantitative data, also known as numerical data, always takes the form of numbers. Quantitative data is typically the result of counting or measuring attributes of a population (e.g., amount of money, pulse rate, weight, number of people living in your town, or the number of students taking statistics). Quantitative data may be either discrete or continuous.
All data that results from counting is called quantitative discrete data. This data takes on only certain numerical values. If you count the number of phone calls you receive each day of the week, you might get values such as zero, one, two, or three.
Data that is composed not just of counted numbers but of all possible values on an interval (the real numbers) is called quantitative continuous data. Continuous data is often the result of measurements like lengths, weights, or durations. The length of a phone call in minutes would be quantitative continuous data.
If we let X equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be a person’s party affiliation, then it would fall into categories such as Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X (for example, calculating the average points earned in class), but it makes no sense to do math with values of Y, as you can’t calculate an average party affiliation.
Example
At the supermarket, you 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 vegetables (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies).
Name datasets that are quantitative discrete, quantitative continuous, and qualitative.
Possible solutions
- The three cans of soup, two packages of nuts, four kinds of vegetables, and two desserts are quantitative discrete data because you count them.
- The weights of the soups (19 ounces, 14.1 ounces, and 19 ounces) are quantitative continuous data because you measure weights as precisely as possible.
- Types of soups, nuts, vegetables, and desserts are qualitative data because they are categorical.
Try to identify additional data sets in this example.
Your Turn!
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