In MapInfo, using Vertical Mapper, I can do a line inspection and get the Max, Min, Mean etc values for a polyline from one or more open grids which is then added as an attribute to the polyline. I'm trying to do a similar process in ArcGIS 10.1 but have been unable to work out which tool I would need to run. Any suggestions, I have access to most extensions including Spatial Analyst and have ArcInfo level licencing.
I would suggest using the Zonal Statistics tool in Spatial Analyst. This will allow you to get the mean, majority, maximum, median, minimum, minority, range, standard deviation, sum, and variety (number of unique values).
While I haven't tried this tool with a polyline input, there is nothing in the help file that indicates that you can't use a polyline.