Not really my point I’m afraid. Their math is wrong anyway you cut it. Read my example above.
>> Their math is wrong anyway you cut it <<
No, as other posters have observed, you apparently don’t understand Lesson Number One about sampling, which is that sample size affects the standard deviation (margin of error), but not the estimated mean. Therefore, I regret to say that it’s YOUR math that’s wrong.
The main point to remember is that an unweighted average of polls is basically OK, as long as the sampling that underlies each subject poll has been performed competently.
On the other hand, a simple average of the standard deviations (margins of error) is definitely not appropriate. Instead, something like a “Pythagoreon average” — weighted by sample size — could be used. But for whatever reasons, the people who compute the Real Clear Politics averages have decided not to publish this kind of number. I guess maybe they think such info simply would be too complicated to explain to the typical reader.
(Still, I wouldn’t be surprised to learn that somewhere in the sub-basement of the RCP building, there’s a statistics nerd who daily grinds out Pythagoreon weighted averages of the standard deviations, either for his own amusement or for use in the RCP’s internal deliberations.)