Well with simple hand movement you reach easily 200° per second, that's not even a turn per second, but yet it's 10% of the fullscale. Really, it's not noise to blame here...If there was noise, he wouldn't get values like 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 0 0 0 -1 -1 -1 -1 -1 2 1 2 1 2 1 2 1, more like 10 15 0 2 -15 -19
Again, what's the value of GYRO_SENSITIVITY ? Also try reading the temperature, take a hair dryer and warm it a bit (not with a finger because of electrostatic discharge) and look if the value is correct.