Mean, median, and mode are each important, each easily mistaken for the others, and, depending on context, misleading or completely meaningless.
I came across a scenario yesterday which highlighted their differences and limitations a little too perfectly:
- Consider every human being in the world.
- List each person’s total testicles.
- What is the mean, median, and mode of that list, and what do they mean?
Is this even worth the trouble? If you aren’t trying to shock or pander to or titillate your students, are testicles fair game? ‘Cause the implications and extensions are really awesome here.
Like: the average human being has one testicle.
Or: the median number of testicles is either zero or two depending on gender majority.
And: the median and the mode will be the same number except under a few (also awesome) conditions.
How do I avoid panicking my principal here?
[via Jim Ray's cool tumblog]