Medians and categorical data
Even though the median may be carefully defined as the middle value in an ordered data set, students sometimes try to find the median of categorical data sets. Students focus upon ordered but ignore numerical. Their thinking needs to be challenged.
Introduce a set of categorical data that has an even number of categories and ask them to find the median.
For example, a class voted on where they would have their end-of-year celebration.
Whether students order the categorical value labels alphabetically or order them by frequency, they will be faced with the dilemma of finding the 'middle' of two places. Being asked to find the middle of, for example, the zoo and the beach, should lead to discussion of the validity of ordering categorical data.
There is further elaboration in Problems with Categorical Data.