How do I generate weighted centroids for ZCTAs using population from census tracts

Question

In ArcGIS 10.1, how do I calculate the weighted centroid of ZCTAs, where I want the weight to be a population from census tracts?

Here is the thing:
1) ZCTAs go out of the boundary of the counties that I'm interested in performing this weighted centroild? Should I clip the ZCTA using the county boundary?
2) The boundaries of ZCTAs and tracts do not nest within each other. And for urban areas, census tracts are smaller, but for rural areas, ZCTAs are smaller.
3) I was recommended using a raster. So I joint the number of population of interest with the shapefile for each census tract, and then calculated the density by dividing the pop by area, and then convert it into a raster layer (after which I got stuck).
And I tried to follow the instructions given by http://gis.stackexchange.com/questions/7789/how-do-i-calculate-a-weighted-centroid-with-respect-to-a-raster-e-g-population and http://forums.esri.com/Thread.asp?c=93&f=993&t=299548. But I'm not sure how specifically should I do (currently don't have spatial analyst tool license). Can I still do it without this license? Or I need to purchase it?

Thanks!

ChenxiaoLing · Answer

This thread below seems to go into some details on how to.

http://forums.arcgis.com/threads/59304-population-weighted-centroid

It was not quite the same, because the boundary of census tracts is not nested within that of ZCTAs, so it is not a 1:1 or 1:N situation. Thus, I'm not able to perform this in vector.

I saw people doing http://forums.esri.com/Thread.asp?c=93&f=995&t=299548 and http://gis.stackexchange.com/questions/7789/how-do-i-calculate-a-weighted-centroid-with-respect-to-a-raster-e-g-population . But I couldn't follow them. Can someone explain the raster/grids part better for me?

Jason_RobinsonRobinson · Answer

This thread below seems to go into some details on how to.

http://forums.arcgis.com/threads/59304-population-weighted-centroid

ChenxiaoLing · Answer

Now I have the license... Anyone help?