Hi Roberto.
I'm sorry you're having some difficulty. Let's see if we can help get this sorted out.
First off, I notice the your input raster is identified as a 64-bit double-precision TIFF. Is this intentional? I don't often come across this particular type of Tiff data. If you use the Copy Raster GP tool to make a new version of the data with the Pixel Type set to a regular 32-bit float, does the resulting raster have the same outcome when used in the Focal Statistics tool?
If you convert your input raster to an Esri GRID format raster and use that as input, does the problem recur?
I did some testing with some local data that I mapped to a value range similar to what you report, but could not produce any unexpected results. Would it be possible to provide a copy of your data to test with? If you could prepare a smaller section of it that still demonstrates the problem, then it would facilitate the investigation.
Thanks,
Juan