Incorrect reasoning in obtaining average family income This is a relatively easy question but I am new to statistics so I hope I could get a better idea. Me and my friend were discussing the following:
My friend said that if someone wants to find the average monthly family income of a country and goes about finding this by saying: if the average family size is 4, I just multiply this by the average monthly income per person.
However, I think think reasoning is incorrect but I can't really explain why.
 A: The United States government does not track "family" income, per se. Rather, the measurement is referred to as "household" income, and it includes the incomes of all individuals in the household over the age of 18. These data are primarily collected by the Census Bureau. Marco makes an important point, namely, that "family" size includes children. Therefore multiplying the average monthly income per person in the United States (or any other country) by four would not provide an accurate estimate of median household income. This would also ignore the fact that men are paid more than women. The Census Bureau also takes race, size of household, and geographic location into account when computing their estimates.
A: Macro is right that it depends on how you define income per person.  Let's assume for simplicity that the income per person in a family is gotten by taking the family income adn dividing by the family size.  Call ci the per person income for the ith family and ni the number of family members in the ith family.  Suppose we have a total of M families.  How would we define the average family income?  It would be
(∑ni ci)/ (∑ni) .  Each sum goes from 1 to M.
Now what your friend suggests is 
the average family size which is Fs=(∑ni)/M
multiplied by the average monthly income per person which is Fs (∑ci/M) = (∑ni)(∑ci)/M^2
Then compare (∑ni ci)/ (∑ni) to (∑ni)(∑ci)/M^2
They are not the same even algebraically.
