I have data in the following form that correspond to data about sessions on a website: ID, # of actions (length), mean and standard deviation of time between actions:
# ct avg stdev 1 8 20 11.4371991243278 2 4 32 18 3 21 24 11.0142252516796 4 6 120 124.817867310734 5 54 12 14.7454698954735 6 4 12 2.08166599946613
What I want to compute is a "typical" standard deviation for a session, possibly weighted. I know that I can compute the standard deviation across all sessions by getting the aggregate second moment from the mean and stdev and subtracting the aggregate mean, but I'm not sure that's what I want.
I want to be able to compare the standard deviation in a particular session against others to see if it's higher or lower. Perhaps one way to do this would be to normalize standard deviations by their mean (giving a percentage measure) since the averages differ significantly and this also affects the magnitude of the standard deviation.
Does anyone have a principled way to approach this?