# What kind of mean to use for a mix of negative and positive percent values?

I've got a question from a colleague about what sort of mean to use in calculating the average of the deviations of actuals from a forecast, which are in percent. The data look(s) like this:

-0.26
-0.21
-0.9
1.56
1.88


For example, the last unit above beat the forecast by 1.88%. My intuition was geometric (based on this question), but I am not sure how to to deal with the negative values.

Edit: I think I've figured it out once I had some more coffee. I think you want to transform the data to (1+percentage). For example, enter +4% as 1.04. Similarly, a percentage of -2% would be .98. Would that be correct?

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Your pre-coffee intution seems to be working well. –  user10525 May 8 '12 at 13:30
Thanks! I'll take advice from you and Arthur F. Burns any day. –  Dimitriy V. Masterov May 8 '12 at 13:49
Why not use an arithmetic mean? Do you think the mean is inappropriate due to your mix of negative and positive numbers? –  Joel W. May 8 '12 at 15:55
I was taught to use arithmetic means for levels, geometric for ratios, and harmonic for rates. My data seems more like ratios or maybe rates (since they are each unit's deviation from from forecast in % during a given period of time). All are pretty close in this case, so it is a bit of an academic matter on which Pythagorean mean to use. –  Dimitriy V. Masterov May 8 '12 at 18:10