Return to Answer

In general, when you have ordinal categories, it is appropriate to use the median to describe the center of the sample, and thus estimate the center of the population of opinions. However, the definitions given in the questionnaire for your categories are numerical. So you might use the mean, if you are careful about its interpretation.

As a practical matter, I wonder how accurately students can guess the true percentage of classes with discussion when they just have to choose one of four intervals on a questionnaire. It seems best to take this approximate mean as saying "Roughly, 56% of classes (slightly more than half) had discussion," rather than as saying, "Exactly 56.195% of classes had discussion."

In general, when you have ordinal categories, say for opinions, it is appropriate to use the median to describe the center of the sample. Thus the median can estimate the center of the population of opinions. However, the definitions given in the questionnaire for your opinion categories are numerical (percentages). So you might use the mean, if you are careful about its interpretation.

As a practical matter, I wonder how accurately students try to guess the true percentage of classes with discussion when they just have to choose one of four intervals on a questionnaire. It seems best to take this approximate mean as saying "Roughly, 56% of classes (slightly more than half) had discussion," rather than as saying, "Exactly 56.195% of classes had discussion."

set.seed(531)
x = sample(1:4, 100, rep=T, p=c(.2,.3,.3,.2))
tabulate(x)
[1] 11 29 36 24
mean(x)
[1] 2.73   # nonsense mean of ordinal labels
median(x)
[1] 3      # median of ordinal labels

set.seed(531)  # for reproducibility
x = sample(1:4, 100, rep=T, p=c(.2,.3,.3,.2))
tabulate(x)
[1] 11 29 36 24
mean(x)
[1] 2.73   # nonsense mean of ordinal labels
median(x)
[1] 3      # median of ordinal labels

Ordinal categorical variable. For example, suppose you have data from 100 were (simulated in R) as follows, using numbers "1", "2", "3", "4" to label the four categories. We have frequencies $f_1 = 11, f_2= 29, f_3= 36, f_4= 24.$

In terms of percentages, my (simulated) students seem to be saying that the percentage of classes with discussion was somewhere in the interval $[51, 75].$

Ordinal categorical variable. For example, suppose you have data from 100 students (simulated in R) as follows, using numbers "1", "2", "3", "4" to label the four categories. We have frequencies $f_1 = 11, f_2= 29, f_3= 36, f_4= 24.$

In terms of percentages, many of my (simulated) students seem to be saying that the percentage of classes with discussion was somewhere in the interval $[51, 75],$ with some saying less discussion and some saying more.