Quantitative Versus Qualitative Data for AP Statistics

Quantitative data, or numerical data are data measured or identified on a numerical scale.

Qualitative data or categorical data are data that can be classified into a group.

Examples of Quantitative (Numerical) Data: The heights of students in an AP Statistics class; the number of freckles on the face of a redhead; the average speed on a busy expressway; the scores on a final exam; the concentration of DDT in a creek; the daily temperatures in Death Valley; the number of people jailed for marijuana possession each year

Examples of Qualitative (Categorical) Data: Gender; political party preference; eye color; ethnicity; level of education; socioeconomic level; birth order of a person (first-born, second-born, etc.)

There are times that the distinction between quantitative and qualitative data is somewhat less clear than in the examples above. For example, we could view the variable "family size" as a categorical variable if we were labeling a person based on the size of his or her family. That is, a woman would go in category "TWO" if she was married but there were no children. Another woman would be in category "FOUR" if she was married and had two children. On the other hand, "family size" would be a quantitative variable if we were observing families and recording the number of people in each family (2, 4,…). In situations like this, the context will make it clear whether we are dealing with quantitative or a qualitative data.

Discrete and Continuous Data

Quantitative data can be either discrete or continuous. Discrete data are data that can be listed or placed in order. Usually, but not always, there is a finite quantity of discrete data (e.g., a list of the possible outcomes of an activity such as rolling a die). However, discrete data can be "countably" infinite. For example, suppose , where n = 1, 2, 3,… Then the first outcome corresponds to n = 1, the second to n = 2, etc. There is an infinite number of outcomes, but they are countable (you can identify the first term, the second, etc., but there is no last term). Continuous data can be measured, or take on values in an interval. The number of heads we get on 20 flips of a coin is discrete; the time of day is continuous. We will see more about discrete and continuous data later on.