Averaging decibels Wikipedia: 

The decibel (dB) is a logarithmic unit that indicates the ratio of a
  physical quantity (usually power or intensity) relative to a specified
  or implied reference level.

If I measure some physical quantity in decibels, then what is the preferred way to calculate the mean of the measured values? Is it enough to simply average them, or should I convert them back to linear scale, calculate the average, and convert it back to decibels (example)? When should I use which approach, and why?
 A: The "physically natural" quantity to average is the actual power, or energy, but it depends exponentially on the number of decibels. So if you were averaging the power or energy, the result would be pretty much equal to the power or energy of the largest (loudest) reading in decibels.
So even though it's physically less natural, you probably want to compute the average number of decibels itself. But as you said, it's abuot "preferences". Your question isn't a question about observables, it's about subjective choices, so there can't of course be any "only correct and objective" answer. For various applications, various averages may be more or less useful or representative.
A: There are reasons more than "preference" for the averaging. You defined it that way usually because you can get more information from that, particular for those additive quantities.
Suppose you preform a set of measurement at a particular point in space, there are two cases: (a) get the averaged value (b) take the average for the intensity itself, and then converted to decibel.
If you have the quantity in situation (b), you can know how much average energy flux passing through that point. Also, you can know the total energy flowing through that point. This information cannot be obtained from the method (a).
Similar situation for the earthquake, if you take the average for the energy, you can know the total energy released by that particular point, which is important. However, you cannot obtain this information by simply taking the average of earthquake scale.
Sure, as pointed out by Lubos, if the variation is small, these two definitions are basically the same as the $\log$ (any) function is local linear, and you can now have additive quantity again.
A: Any value can be convert in dB.
So if I have two sets: A and B that weighs respectively 2 and 5 kg.
Let's convert them in dB.
   a = 10 log10( 2 ) = 3,0103
   b = 10 log10( 5 ) = 6,9897
So if we make an average on the dBs values we obtain
AVG(a,b) = 5kg ! which is clearly wrong.
The correct AVG should be done on the linear values and is 3.5 kg.
So, doing average on unknown physical information can led to misleading conclusions !!! If we measure values that are exponential or logarithmic but without the knowledge of the operator... we can just don't understand the underlined logic !
A: To determine the expected power level from 2 or more signal sources to be combined and measured in real time, the level of each should be converted to linear values, the linear values averaged, and that value converted back to dB.
To do statistical analysis of multiple measurements, use decibels without conversion.  Example below.
The following chart shows a set of values in decibels (blue line).  The dashed lines are the average values calculated

*

*(red) using dB values

*(green) by averaging the linear values and converting it back to dB.


The decibel unit was created to avoid problems using linear power values having a scale that covers many orders of magnitude.  Using linear values in a simple formula like Cpk produces a value dominated by the largest value.
A: To Pierre Ghislain's answer: AVG(a,b) is not 5kg but 5dB, which converts back to 3.16kg – and he's right, that's not 3.5kg.
In my opinion it depends what the 'average' should express.
(a) If you have two loudspeakers, operating in phase-sync and you want to compute the average output in pascal (for sound pressure), you need to convert the dB back to pascal (or whatever your original unit was) and average the values.
(b) If you have made several measurements of e.g. loudness in dB at different times of the day and you want to know the average 'loudness' during a day (in dB) you will average the dB values as if they where linear numbers, to get an average dB value.
This is nicely illustrated by the two lines that user313951 showed
A: Utilizing the average of a dB value is wrong.  The dB being a mathematical artifact to derive a "unit" of measure where you compare value vs a reference (pressure, voltage etc.) and you are able to observe it in a great range as you are spacing it by an exponent (the log operation).  To give you the idea, averaging 1dB with 3dB is not (1+3)/2 = 2db, that would be equivalent to saying that 1+100 averages to 10, where you know that the result is over 50. Now depending on if you are dealing with Power or Amplitudes values the math is pretty similar and easily deductible. (this is my first post here thus I'm not sure how to put you a formula here, but I hope this brings you or whoever gets here because of your question to the right direction of thought :)   )
