Looks like the idea works. I've group the samples into seconds (20 samples per second), and flag each second as "active" or "inactive" based on the difference between the max & min acceleration values within that second. That is, if the difference is above a certain threshold, then we have movement.

It's quite obvious in this graph that this works quite well, and helps us keep the data manageable. You can also see that even when standing or sitting, there are some 1-5 second periods of activity, as I was moving my mouse, and simulated coffee drinking and talking to the phone. But, looking at the graph, it should be really easy to distinguish walking and these random, momentary movements.