- Determine whether a value calculated from a group is a statistic or a parameter
- Identify the difference between a census and a sample
- Identify the population of a study
- Determine whether a measurement is categorical or qualitative
Quantitative or Categorical
Once we have gathered data, we might wish to classify it. Roughly speaking, data can be classified as categorical data or quantitative data.
Quantitative and categorical data
Categorical (qualitative) data are pieces of information that allow us to classify the objects under investigation into various categories.
Quantitative data are responses that are numerical in nature and with which we can perform meaningful arithmetic calculations.
We might conduct a survey to determine the name of the favorite movie that each person in a math class saw in a movie theater.
When we conduct such a survey, the responses would look like: Finding Nemo, The Hulk, or Terminator 3: Rise of the Machines. We might count the number of people who give each answer, but the answers themselves do not have any numerical values: we cannot perform computations with an answer like “Finding Nemo.” Is this categorical or quantitative data?
A survey could ask the number of movies you have seen in a movie theater in the past 12 months (0, 1, 2, 3, 4, . . .). Is this categorical or quantitative data?
Sometimes, determining whether or not data is categorical or quantitative can be a bit trickier. In the next example, teh data collected is in numerical form, but it is not quantitative data. Read on to find out why.
Suppose we gather respondents’ ZIP codes in a survey to track their geographical location. Is this categorical or quantitative?
A survey about the movie you most recently attended includes the question “How would you rate the movie you just saw?” with these possible answers:
1 – it was awful
2 – it was just OK
3 – I liked it
4 – it was great
5 – best movie ever!
Is this categorical or quantitative?
Again, there are numbers associated with the responses, but we can’t really do any calculations with them: a movie that rates a 4 is not necessarily twice as good as a movie that rates a 2, whatever that means; if two people see the movie and one of them thinks it stinks and the other thinks it’s the best ever it doesn’t necessarily make sense to say that “on average they liked it.”
As we study movie-going habits and preferences, we shouldn’t forget to specify the population under consideration. If we survey 3-7 year-olds the runaway favorite might be Finding Nemo. 13-17 year-olds might prefer Terminator 3. And 33-37 year-olds might prefer . . . well, Finding Nemo.
The examples in this page are discussed further in the following video:
Classify each measurement as categorical or quantitative.
- Eye color of a group of people
- Daily high temperature of a city over several weeks
- Annual income