I have a shp file with some rectangles and I want to extract statistics within these areas from a raster image. I prefer ArcMap 9.3.
As a free alternative, SAGA GIS contains a module that may do what you want (Grid Statistics for Polygons). http://www.saga-gis.org/saga_modules_doc/shapes_grid/index.html
You can also use GRASS for zonal statistics. From doc page:
r.statistics is a tool to analyse exploratory statistics of a "cover layer" according to how it intersects with objects in a "base layer". A variety of standard statistical measures are possible (called "zonal statistics" in some GIS).
The available methods are the following:
- average deviation
- standard deviation