And half the parents are above average

The Times;' Landon Thomas has a story today about welfare benefits in the UK that are not means-tested -- for example, every household with children under 20 gets a child support allowance, regardless of income. One sentence knocked me off-topic into Deep Math:

Research shows that, although payments are promoted as a direct and simple means to allay child poverty by putting money into the hands of needy mothers, nearly half of the payments go to families with above-average incomes.

I suppose a disproportionate percentage of high income families may not have children at home, and that wealthier families may have fewer children on average, so that statement is not as tautological as it may appear.  But still.