Thanks, I think I see the problem now. It seems that you have two different shapefiles (Census Block and Urban/Rural.) The geographical boundaries for the block and U/R areas are not the same. I assume you want to find out how whether Census Blocks with populations of 50,000 are all urban or some similar geoinquiry. This is a subject about which I am beginning to learn, but am not fully knowledgeable.
In the Spatial Analysis MOOC, the instructors introduced the concept of MAUP error. It kind of means that you need to be careful when analyzing geographical areas that have dissimilar boundaries. In the MOOC, the instructors taught us a little about using the weighting tools to overcome potential MAUP error. I am incompetent to be able to give you much advice here except maybe to look in Geographically Weighted Regression (GWR)—Help | ArcGIS for Desktop, and depending on how you have tagged this Geonet question, you might tag some other forums like Spatial Analysis to see if they will offer help. Sorry, if I have misunderstood your question.
And I hope you solve your geoinquiry.