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A margin-of-error question

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On the Ed Show tonight, Jonathan Alter tried to rain on Ed and Richard Wolff's pre-election parade by cautioning them not to become over-confident about Ohio because the polls show Obama's lead to be still within the margin-of-error.

Yet, is the concept of margin-of-error really valid when one is talking about an average of polls as opposed to an individual one? Obviously, each individual poll has a margin-of-error based on the number of people who respond to the question. So, if one poll shows Obama ahead with likely voters in Ohio by, say, 3 points, and the margin of error is +/-3, then he might either be tied with Romney or ahead by 6.

But if Obama is ahead by an average of 3 in, say, 10 polls, isn't it pretty obvious that he's ahead by 3 in the state, since, theoretically, for every poll that shows them tied, there would be one that shows Obama ahead by 6 points, far outside the margin-of-error for a tie? Doesn't the concept of margin-of-error dissipate as more and more polls are brought into the equation? As a non-math/statistics person myself, I honestly don't know the answer to that question, but something struck me as off about Alter's reasoning.

Anyway, here's the clip, with the discussion on this issue beginning at around the 8:30 mark.

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