Here's a joke for you:
Bill Gates walks into a room and everyone becomes a millionaire, on average.
Hilarious, huh?
I see the mail piling up right now: "Dear Mathman. I don't get the joke." or "Dear Mathman, it's too hard to understand that joke." or even, "Dear Mathman, that's a dumb joke. Pencil tapping is waaayyy cooler." (maybe if you're actually really good at pencil tapping)
Well, it isn't a dumb joke, because you have to understand the three M's to get it. What are the three M's you ask. Is that, like, 150% better than Eminem? (most certainly). Do they melt in your mouth, not in your hands? (It does take a long time in the microwave to melt the candy shell, but that's a story for another time.)
The three M's are measures of central tendency, or the mean, median, and mode. Measures of central tendency (the three M's), refer to "average". Most people get the mode. That was a bit of a joke in itself as mode refers to the most frequent data values in a set. That doesn't help us much with the Bill Gates joke since he's probably the only one person in the room with enough money to buy a planet.
The median refers to the middle value of a data set. Once again, since Mr. Gates is only one data value, one person with no money in their pockets would cancel his cash right out.
That leaves mean as being the only hope to make this joke funny. Never underestimate the power of an outlier. A quicky wiki left me with Bill being worth somewhere around $58 billion in 2008. That's $58,000,000,000 in standard notation or 5.8 x 10 to the 10th power dollars. Do you realize how big that is? That's 58,000 groups of $1,000,000 each. That's enough cash to pay someone (who's awesome at it) to pencil tap for you while you do your math homework.
Since it takes $1,000,000 to be a millionaire, Bill Gates could offset 57,999 other people in the room who wouldn't even have enough money to buy their own pencil to tap and pull the mean to $1,000,000 a piece. That would buy a whole lot of pencils for each person so they could stop absconding them from Mr. Krack's pencil box.
Here's the definiton for mean:
sum of all the values
--------------------------- = mean
total number of entries
In our case:
$58,000,000,000
------------------------ = $1,000,000
58,000
Just to put that in perspective: Heinz Field seats 64,000 people. That means we'd need 64,000-58,000 = 6,000 more millions of dollars to make everyone in Heinz Field (on average) a millionaire. That amount of money we'd need to spread over 63,999 people is 6,000 x $1,000,000 = $6,000,000,000. So the average amount those (other than Bill Gates) 63,999 people would need is $6,000,000,000 / 63,999 = $93,751.46. I'm taking a guess here that most people don't have this much money kicking around. (Personally, I am good for the $.46 of my share.)
To me that makes this problem even more interesting since Bill himself could cover 58,000 out of the 64,000 people in the stadium and most likely we still wouldn't be able to make everyone in the stadium millionaires since we wouldn't have enough money.
One man has the capability to make the "average" of:
58,000
----------- = 90.625%
64,000
of the population of Heinz Field millionaires, while the rest of us 63,999 people would have a hard time covering the remaining 9.375% of the money to raise the average of the population of Heinz Field to the status of millionaires.