> On Fri, 02 May 2014 10:51:01 -0600, Donald Sauter > <email@example.com> > wrote: > > > From the beginning, my concern has been with the > relative worth of the > > mean, median, and mode as standalone values. > > None of them has "standalone value", and I don't see > why anyone would > think that any of them does. > > Why would anyone assign meaning to a summary given > context-free? To > suggest that people who understand their value would > do so is foolish. > > - --Louis A. Talman > Department of Mathematical and Computer Sciences > Metropolitan State University of Denver
No, no, really, it's not so hard to grasp. If someone tells you the average amount of money in the pockets of 10 kids is 57 cents, you know 57 cents could stand in for all 10 actual amounts; that if they cobbled their money together they'd have exactly $5.70 and could buy a pizza, maybe.
What a nifty little statistic.
If you're told the median amount is 57 cents, you might conclude that the total amount of money in their pockets is between $3.42 and infinity.
If you're told the mode is 57 cents, you might conclude that the total amount is between $1.42 and infinity.
Why I say "might" is because, if you allow for the possibility of IOUs in their pockets, the lower bounds for the median and mode cases become minus infinity. Thus, we can state--with absolute certainty--that the kids are somewhere between infinitely wealthy and infinitely in debt.