Is there anyway to establish an Average function that adjusts to only
populated fields?

Example:

I have a spreadsheet established that pulls from 12 other sheets. As a
conseqence,the fields on this sheet only update each month (the other sheets
are monthly sheets, and thus each one is used within the appopriate month).

I would like to AVERAGE the fields on the13th sheet, showing a monthly
average of the values derived from the other 12. However, I want the AVERAGE
to reflect only the populated fields, so that I receive an accurate "running"
average. Ex: if only January and February have data, then the average would
be divided by 2, not all 12 fields.

Is there any way to accomplish this? I figure it is a combination of the IF
and AVERAGE formulas, but I've no idea how to do this.

Thank you in advance.