A colleague brought to my attention documentation for a standardised questionnaire which recommended using the median and interquartile range to describe summary variables created by combining responses to multiple questions. In most instances these summary variables had 20+ possible values (e.g. the sum of responses to 5 questions each on a 0-4 scale resulting in a 0-20 scale).
Strangely, this advice also applied to single item summaries of yes/no questions - i.e. the new summary variable is just the response to a yes/no question. Clearly, for a binary variable such as this the median + IQR gives much less information than reporting the proportion of 'yes' and 'no' responses. My question is - how many levels would a variable require for the median + IQR to be an informative summary of the central tendency and spread of that variable?