Minimum Area Bounding Ellipses... containers for geometry
The link to the ArcGIS Code Sharing site... ... pictures are worth more than words.
The toolset is easy to use. There should be some expectation that your point sets can be enclosed with an ellipse or some other container.
For non-degenerate ellipses, you need at least 3 points, since 3 non-collinear points is the minimum that esri's geometry engine will allow you to create polylines and polygons in.
My Bounding Containers toolset covers other 'containers' to put stuff in. Clean up your data and put it in its place 
So here is a pretty picture, showing some simple cases of point groupings and their generated ellipses.
This is not the same as the Standard Deviational Ellipse. That one doesn't enclose the boundary... it is a stats thing.
Just an example of the details from above
Then you get this... you can see it can't you...
Large data clouds are not problem and it is nice to see an elliptical cloud being delineated as an ellipse
Enjoy
Send me emails if you have questions