In this example, a relationship is determined between students and study sectors.  Students being a point layer and study sectors being a polygon layer.  Determining the number of students within each sector is easy to do by simply counting the visible points for each area.  The is not always correct as some points can fall on top of each other.  You can use the select by location tool to find the exact number of student within each sector, but this can become time consuming if you have a lot of areas to cover.  The solution to this problem is the spatial join tool.  This tool determines the spatial relationship between the polygons and points.  A point count for each polygon is created and placed in the attribute table.

Here is a demonstration video:

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Download the video to your computer: ArcMap Spatial Join Tool