Meanness
You'll never hear more about the 'average
family' than you will at budget time. "The average family is doing better
under this government than any other!", they'll say.
It could be true. Look at these incomes for
five families in Vespuccia:
Family |
Income |
Greens |
2000 |
Blues |
2000 |
Pinks |
2000 |
Oranges |
2000 |
Grays |
92000 |
Compare to these five families in Pareconia:
Family |
Income |
Greenies |
20000 |
Bluies |
20000 |
Pinkies |
20000 |
Orangies |
20000 |
Grayies |
20000 |
Those of you who
haven't seen this trick before may have whipped out your calculators, added all
the Vespuccian incomes together, divided by five, and got 20 000. Then you did
the same for Pareconia and got-- 20 000.
The same average!
So they must both
be doing equally well, right?
Of course not! 4 of
the five Vespuccian families are at the edge of starvation, while one fat cat
is laughing away. The Pareconians, on the other hand, are doing okay for
themselves.
What is the lesson?
That averages lie?
Well, yes, but
that's not the whole story. Those of you who have seen this trick before
answered my question with a question: What kind of average?
There are three.
The mean is the kind we took, where you add all the numbers up and
divide by the number of samples. The mode is the most frequently
occurring number. The median is the number for which there are an equal
number of samples above and below.
(Answer: 2000 for
both)