1.2 Data Basics
Types of Data
Data may come from a population or from a sample. Lowercase letters like x or y generally are used to represent data values. Most data can be put 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 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+.
Quantitative data are always numbers and is often called numerical data. Quantitative data are typically 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 made up not only of counting numbers, but of all possible values on an interval (the real numbers) are called quantitative continuous data. Continuous data are often the results of measurements like lengths, weights, or times. The length, in minutes, of a phone call 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 some categories include Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X (calculate the average number of points earned, for example), but it makes no sense to do math with values of Y (calculating an average party affiliation makes no sense).
Example
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.
Your turn!
Levels of Measurement
The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level):
Data that is measured using a nominal scale is categorical data where the categories have no natural order. Colors, names, labels and favorite foods along with yes or no responses ar