If you have access to an Advanced license you can use the Near tool. ArcGIS Help (10.2, 10.2.1, and 10.2.2)
You would use the surrounding points as input features and the population points as near features.
This will add information to you surrounding points about the population point that is nearest (field NEAR_FID). Next you could summarize on that field to get the number of surrounding points located near a population point. Join this number and the population to the surrounding points and divide the population by the number of points.
If you don't have access to an advanced license, you could use a spatial join. ArcGIS Help (10.2, 10.2.1, and 10.2.2)