Government statistics show that the real (adjusted for inflation) average income for families has risen over the last five years.
Conclusion (therefore)
The Anderson's real income (adjusted for inflation) must have increased over the last five years.
Evidence (since)
Government stats show that real average income for families has risen over the last five years.
The Andersen family's income is average for families.
Evaluate
This seems to be some sort of mathematical flaw, playing off two different usages of the word "average". Let's flip into objection mode:
Given that ... the Anderson's have a family income that is average for families (like if the average family income is $100k, their family income is $100k),
and given that ... average income for families has risen over the last five years.
How could we still argue that .... the Anderson's income has not increased over the last five years?
Well, naturally when we hear , that does not mean that all families' income has risen. Some have gone up. Some have stayed the same. Some have gone down. But overall, once you average all those stories together, the average has moved up.
So we can seemingly just say that the Anderson's weren't lucky enough to be beneficiaries of this recent trend of rising family income. Maybe they also had a family income of $100k five years ago. Maybe they even used to make $180k, and then Mr. Anderson got laid off, and now they're only making $100k.
Goal
The fact that the Anderson's currently have the average family income doesn't mean that their family income has behaved as "average family income" has over the past five years.