I had a tool I made that basically did this, so I just tweaked it a little to fit what you need.
It's called Calculate Point Statistics, and you can download it here:
http://ianbroad.com/downloads/CalculatePointStatistics.tbxhttp://ianbroad.com/arcgis-toolbox-calculate-point-statistics-polygon-arcpy/
Source code:
http://ianbroad.com/downloads/scripts/CalculatePointStatistics.pyhttp://ianbroad.com/download/script/CalculatePointStatistics.py
It takes an input Polygon and Point feature class and uses a selected field to find the minimum, maximum, and average of the points and adds the results to the polygon feature. It skips any null values. It will work with ArcGIS 10.1+
Here's a screenshot of the parameters: