Innumeracy, big time

A New York City-based organization called the Coalition for the Homeless is currently running a TV public service announcement in which they say:

Which is more disturbing: That each night in New York City, more than 40,000 people are homeless, or that the average age of a homeless person is 9?

(Or something to that effect. I'm paraphrasing, but the figures are quoted accurately.)

If the avarage age of 9 strikes you as implausible, you're right. The very same Coalition for the Homeless lists the following as one of the basic facts about homelessness:

In New York City... Each night more than 40,000 people--including more than 16,000 children--experience homelessness.

This basic fact makes the average age of 9 an arithmetic impossibility. 16,000 is 40% of 40,000; so even if each age category (children and adults) is assumed to have the lowest average age possible (1 and 18, respectively), the average age of a homeless person would be 11. But of course these assumptions are empirically completely implausible, which means that the average age of a homeless person is not only certainly greater than 9, but most likely much more so. Assuming group averages of 3 and 30, for example, gives an overall average of 19. The only nationwide data that I have been able to find is here, from which the average turns out to be about 32 (see Exhibit 5-3 on page 43).

How's that for innumeracy?