When I was in a train station in France, I was leaving a public washroom and took the photo shown here of a quick survey (under the sign) that they wanted people to fill in before or after drying their hands in one of the two white hand dryers you can see in the picture. People are being asked to push one of the three colored buttons to indicate how satisfied they are with the cleanliness of the bathroom.
This struck me as a wonderful example to bring into our discussions about data types, measurement scales, populations, and samples.
a) What is the population in this case?
b) What type of data are they going to get? Use the categories we saw in class when answering this.
c) What scale of measurement applies here?
d) Could you take an arithmetic mean or calculate the standard deviation of the data they will collect? Either way, what does your intuition or prior knowledge tell you might be more useful for describing those data? (We’ll see more on this later. I’m just trying to point out how some descriptive measures can be less well suited to some data types and/or measurement scales.)
e) Data type and measurement scale aside, how ‘good’ a sample of the population do you think the train station managers will get in this situation? I can think of at least two good reasons why it very likely won’t be representative of the actual population. What are those reasons? And which one of them in particular is likely to very significantly bias the results of their experiment?