The noise density of the accelerometer and gyroscope data is irrespective of the output frequency. The values are specified in the data sheets of the various products. However, if it is desired to have a lower RMS noise, it is possible to lower the output rate of the data. The onboard algorithms will integrate the data over a longer period of time. This has two effects: the RMS noise lowers but on the other hand, it lowers the bandwidth which means that movements with a bandwidth higher than 50% of the output data rate cannot be detected (but they are integrated in the data).
To show this, an MTi lying still for 10 seconds was configured to output acceleration data at 400 Hz, 100 Hz, 10 Hz and 1 Hz. The difference in the noise is clear. The standard deviations that correspond to these 4 output data rates are:
400 Hz: 0.0137 m/s2
100 Hz: 0.0068 m/s2
10 Hz: 0.0022 m/s2
1 Hz: 0.0007 m/s2