Okay, so here's the situation.
My original raster has a range of values from 180.8 to 4132.9.  The output raster after running the focal statistics has a range of values from 256 to 3969.2.  The focal statistics script I ran was:
FocalStatistics("RASTERNAME",NbrCircle(1500,"MAP"),"MEAN")
There appears to be no outliers in my data.  Now, could NoData cell values be causing this error?  If so can I run the following to correct for the problem?
FocalStatistics(Con("RASTERNAME","RASTERNAME","",FocalStatistics("RASTERNAME",NbrCircle(100,"MAP"),"MEAN")),NbrCircle(1500,"MAP"),"MEAN")
I think this script would fill the NoData values with an average value calculated by the neighborhood created.  Maybe I am wrong.
I am sorry if I am not making too much sense, I am very new to working with rasters, much of my experience is in vector-based GIS work.