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

1. What is the average income in Vespuccia?
2. What is the average income in Pareconia?

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.

3. What is the median income in Vespuccia?
4. What is the modal income in Vespuccia?

(Answer: 2000 for both)

5. If you wanted to present a high income for Vespuccia, which average would you provide?
6. Which do you imagine governments provide?
7. Does an average family have to exist for it to be referred to?

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