Statistics are primarily required to enable the system to better display that data especially when the imagery is 16bit or 32bit. When they are not being used for specific analysis, approximate values are sufficient. When creating statistics of a mosaic dataset that has overviews then the simplest is to set the skipfactor to a sufficiently large value so that only a representative number of samples are used. In many cases the simplest way to do this is set skip factor to the total width of the mosaic dataset / 1000. This will then compute very fast based on the overviews, but contain only approx values. If the mosaic dataset contains a lot of no data areas you may want to set the processing extents to a suitable sample area first. The alternative in V10.1 is to use the 'Data Management Tools/Raster/Raster Properties/Set Raster Properties' tool just set the stats to known values. This takes as input an XML file that defines the stats. Such XML files can be created by using the Save As XML option in the Symbology tab of any raster layer. Then if necessary edit the values. For example in elevation for the complete globe simplest is to set the Min as -450 and max as 8700 with a mean of 400.
