Q:

Is my accelerometer precise enough?

I have a device with an accelerometer and I want to make it as precise as possible (using algorithms). Currently no DSP algorithm is running - I am reading values as they are. I've made 3 tests - in each I rotated the device around one of the axes and recorded the values coming out from accelerometer. It would be perfect if each of the tests would produce a perfect circle; this would mean no further calibration is needed. The desired precision is +- 10mg (+- 1%). For example, the mean value when Z axis is maximal is 1024mg. 1010mg would be acceptable.
Below are the results of tests (Matlab copy-paste to display). Is it enough to test the three axes or should I also test the cases where the gravity gets distributed in all of the axes? Further; what approach would you suggest considering calibration to 1% precision (please be specific).
I need a thorough answer on this topic. 
Rotation around X axis:

Round Y axis:

Round Z axis:

A:

Typically you can improve performance by analyzing the data that you want and analyzing the data that you don't want. I would assume that a plane can't turn infinitely fast so the actual "want" data is properly fairly band limited. Depending on how fast you are sampling the accelerometer you may pick up a lot of "out of bandwidth" noise. This could easily be improved with a low pass filter or some moving average contraption.  The more you know about the properties of the actual signal and the properties of the noise, the better you can separate the two.

