stat: Quartile methods

[StephenG1CMZ]

My maths class was a long time ago, so maybe I am remembering wrongly. But I seem to recall that which definition you should use for the middle of an odd-sized list depended not on culture (which we were not aware of pre-Internet), but on application. For some applications like shoe sizes you might choose one of the two middle values. For other applications you might average them.

In the past when calculators only handled numbers it was only possible to return a numeric value - and whichever number you choose is always going to confuse someone with a different assumption or mode setting.

I would propose that the least confusing value to return on a modern calculator is not some random number depending on some probably unspecified mode setting hidden in one menu or another depending on which calculator you have. The best value to return is a list containing the two numbers of interest. A list containing two middle numbers for odd-sized lists (and for consistency a list containing one number for an even sized list).


That way there are no unexplained mode settings and no pupils getting different answers!

Once you have that list of one or two numbers visible to the pupil, the pupil can decide whether to use one or the other, or choose one at random, or calculate the average. All simple clear and explainable maths depending on the application. No hidden mode settings necessary.