I was examining the small print on a shoe box in order to determine whether the shoes were made of real leather or faux when I encountered the following statement: "Average Contents: 2."
This was rather disturbing, suggesting that some boxes may contain more than two shoes and some may contain fewer. In order to make a wise decision about my purchase, I need to know the range of values and the standard deviation.
A shoebox containing negative number of shoes is difficult to envision, so let's set the lower end of the range at 0. What, then, is the highest number of shoes that could fit in the box?
The answer would depend, of course, upon the size of the shoes. The box in question could not accommodate more than four of my son's size 14 shoes, but what if you used toddler-size shoes? Barbie shoes? Shoes designed for unicellular organisms? The number could easily reach into the millions.
Now suppose you are the unlucky shopper who takes home a box with only one shoe in it. If $69.95 is an absurd amount of money to spend on two glorified sneakers, it's doubly absurd to spend that amount on only one, so naturally you will return to the store and complain. The store manager, in turn, will point to the small print on the shoebox and say, "What are you complaining about? It says right here that 2 is the average number of shoes in a box. Actual numbers may vary. Some settling of contents may occur. Void where prohibited. Have a nice day!"
But then suppose you take home the box containing 1,000,000 shoes visible only with a high-powered microscope. Lucky you! You've struck the jackpot! Your unicellular organisms will worship you! But what are you going to put on your own feet?
Since I'm interested in buying neither one nor 1,000,000 shoes, I'm not sure what to do with the phrase "Average Contents: 2." If I want to find really useful information on a shoebox, these shoes are made for walking--to another store.