## On the average . . .

**T**he
pointy-haired Überboss -

*capo di tutti capi* - marched into the employees' union meeting
and point blank stated

*"Half of you are under average!"* . This got the union guys
protesting and spluttering before they'd had time to think (i.e. their usual mode is protest then
think later about what they're saying ;-)

So I butted in with *"Correct, that's one definition of average ;-)"* and then went
on to point out
*"But what's worse is that the pay of the average employee is less than
the average pay! You're not paying us fairly!"* This of course got the shop
stewards and unionised mob into more of a misty red rage.
But it's true, here's an example :-

The company has 8 blue-collar workers on 10€/hour and 7 white-collar
guys on 20€/hour and 5 bosses on 100€/hour. So the average salary is
(8*10 + 7*20 + 5*100)/(8+7+5) = 720/20 = 36€ per hour.
This kind of *average* is called the **mean**.

Note that most people (15 out of 20) earn less than the mean.

Now certainly the 5 bosses wouldn't (want to) be described as an average employee,
and since there are 8 blue-collar workers as opposed to 7 white-collar ones, the
average employee is a blue-collar worker. And 10€ are less than 36€.
This kind of *average* is called the **mode**, i.e. the class of employees
having the most members.

Another way of finding the average employee is to sort the employees by pay,
first the eight
10€/hour guys, then the seven 20€/hour guys, and finally the five
100€/hour bosses. That's twenty people in total. So the average guy -
the one in the middle - is the 10th one, a 20€/hour white-collar guy.
And 20€ are still less than 36€.
This type of average, the middle member of an ordered set, is called the **median**.

So all I'd said was that the median and/or the mode were less than the mean.
And this is always so when the distribution is skewed like this; it's nothing for
the union guys or the pointy-haired boss to get heated about. In fact if you look
at a company like Microsoft, the distribution is almost L-shaped, due to Bill Gates
earning an obscene amount of money by seriously overcharging
us for his *distinctly* average products :-(

And the moral of today's tale? When someone says *"average"* make sure you
know which one he means:
**median, mode, or mean**. And *why* he chose to use that one!

Copyright ^{©}
Stu Savory
on 22nd September 2007 at 06:22 CEST
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