There are many different terms and methods that 
programs use to shrink images.

Basically, one method picks one out of x pixels 
when you shrink to make an image; result is a 
grainy image (unless the scan is super, super 
clean to begin with).  The other method uses 
information from each pixel to generate a whole 
new image; result is non-grainy.  There are just 
way too many names to describe each, and there 
are many names for the formulas used for the 
latter method.

The graphics program you're using probably has 
different ways to shrink images.  Just gotta find 
the right function.

For an example, try opening up a decent sized 
image in a recent version of Acdsee.  Click edit.

If you click zoom-out, the image becomes grainy.  
That's what you're probably seeing.

Now go back to the original 1:1 image size by 
clicking zoom-in.  Click resize.

Choose a different size and hit OK.  Lanczos 
filter (default) is my personal favorite to use.  
The resultant image should not be grainy.  (Make 
sure the resultant image is at 1:1 size, 
otherwise it'll show up as grainy when it really 
isn't.)

I use Acdsee to generate thumbnails.  Usually 
when you do a non-grainy shrink, the thumb does 
look blurry.  However, the lanczos filter 
eliminates quite a bit of the blurriness.

Hope that helps, later.