Is the average of acceleration magnitude valid? I am doing two tasks of flipping card and lifting a load. I am collecting data for this two tasks for a week. I want to find the mean acceleration for each day. As it is 3-axis I thought it is good to take magnitude.
I have a 3-axis accelerometer sensor. I have the 100 readings collected. I found the acceleration magnitude for each record by using formula:
  $$\sqrt{a_x^2 + a_y^2 + a_z^2}$$
I would like to find the total average acceleration of my readings. Should I find the average of the magnitude of acceleration? 
Can I find it by dividing the sum of values by 100 or (sum of magnitude values)/time?
Is it valid ?
Any suggestions or help is greatly appreciated.
 A: Average acceleration seems like it would only be useful for finding overall change in velocity. If you take the magnitude, then you can get the total change in speed. If you want much of anything else, you should integrate in time. 
A: There is an important consideration here. When are the readings from your accelerometer collected? Are the readings correlated in any way to periods of large acceleration or small acceleration? If so, your readings will be skewed. I'm going to suppose that your accelerometer gives readings every $0.1s$ for instance, and that this time interval does not correlate with the flipping of cards or lifting of loads (i.e. you aren't doing something strenuous every $0.3s$ exactly). In other words, that the readings are essentially at random times.
You can divide the sum of the magnitudes by the number of readings. This will give you an estimate of the typical or mean magnitude of acceleration experienced throughout the period of measurement. This quantity is useful if, for instance, acceleration is putting stress on the equipment. This measure of mean magnitude gives you an idea of the average amount of acceleration/force that is being experienced without caring about its direction.
However, if you want to know the magnitude of the mean acceleration, then this is a different question! It's first necessary to calculate the mean acceleration in the form $(a_x,a_y,a_z)$ (again, divide by number of samples) and then take the magnitude. The magnitude of the mean probably isn't as useful, because the mean acceleration is a measure of what constant, directed acceleration $(a_x,a_y,a_z)$ experienced over the entire duration of measurement would result in a final velocity equal to that predicted by the changing measurements.
Whether you use the mean magnitude or magnitude of the mean depends on the information you want to know.
