Hi Michael
I think this can be achieved by using spatial joins. First you need to use
a spatial join between the polygon and "all points" shapefiles. This will
summarise the point values within each polygon. Next you can create a
spatial join between your centroid file and the polygon file to get the
summarised values from the all the points which would now be stored in the
polygons.
Not sure how familiar you are with spatial joins, so to start you
right-click on polygon data, go Joins and Relates/Join.. then select the
option to "Join data from another layer based on spatial location"
The rest is really self explanatory but this process should work.
Good luck.
Regards
Mervyn