The Google Webmaster Blog and Google Analytics Blog announced they are changing how they define the average position in the search query report in Google Webmaster Tools and search optimization report in Google Analytics.
The new definition will take the average of the top ranking of your site for all searchers, as opposed to all URLs listed and average that. In the past, they would take all the positions of your rankings and average them together, now they are taking only the top positions.
Here is how Google explains it:
Let’s say Nick searched for [bacon] and URLs from your site appeared in positions 3, 6, and 12. Jane also searched for [bacon] and URLs from your site appeared in positions 5 and 9. Previously, we would have averaged all these positions together and shown an Average Position of 7. Going forward, we’ll only average the highest position your site appeared in for each search (3 for Nick’s search and 5 for Jane’s search), for an Average Position of 4.

Historically, this won’t impact the reports but going forward, Google will use this new calculation for determining your average position.
Google said, “we anticipate that this new method of calculation will more accurately match your expectations about how a link’s position in Google Search results should be reported.”
Here is where the average position shows up in Google Webmaster Tools:
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Here is where the average position shows up in Google Analytics:

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smoke + mirrors.
Presume this is only the average of true natural results, rather than hard coded results (ie: Google+, Places, News, Shopping etc)
That makes so much more sense than the old method which looks like it penalizes sites who appear multiple times (even if Google chooses to show them). If anything this is is a correction of the way it should have worked originally. Now they just need to make the data accurate and trustworthy enough for us to actually care.
This is a good example of how Annotations in Google Analytics can be useful.
Add a shared annotation on this date which links to the Google blog post so people will remember when the data calculation changed and what the impact was.
@Mike I’m finding the data pretty accurate now (when using the filter facility to get rid of image search ranks). Are you still seeing inaccuracies?