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The variance on the mean should properly be calculated as
sigma/sqrt(n) for a selected set of random samples.
But I don't think that is valid in this case because the samples are correlated.
Vernier's
software may even be doing some smoothing and approximation for angular
positions that fall between the position encoder's discrete digitization
steps.
We're collecting 20 data points per second. The interaction takes about a
quarter of a second. Students take the 5 data points before and the 5
points after the "collision" and look at the mean angular velocity for
each.