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RichardKennaway comments on [draft] Generalizing from average: a common fallacy? - Less Wrong Discussion
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The average human has one ovary and one testicle.
If your feet are in a bucket of ice and your head's in a oven, on average you're at a comfortable temperature.
The average family has 2.4 children.
And as for correlations, some years ago I wrote this brief note on how little predictive use you get from the typical magnitude of published correlations.
You probably know the story of the three statisticians hunting a tiger? The first statistician's shot goes wild, one meter to the left. The second statistician applies a correction, but overcompensates and misses, one meter to the right.
And that's when the third yells "Got 'im!"
Ya... i need to expand on that in the post - we have that sort of understanding of how the averages fail ('average temperature in a hospital'), but we don't seem to apply it well to correlations (which are still just averages).
edit: your brief note is great. You can expand on something popular - e.g. IQ tests - consider different IQ scores and what they actually tell about probability of individual doing this well or this badly on another IQ test (using correlation between 2 IQ tests). Or assuming that there is some 'IQ' that IQ tests correlate with, what does IQ test actually tell about the IQ.