Attached is a sample time series of observations in 8 categories. I want to calculate the dispersion of these observations in both dimensions (time and category). I have approached this problem from a few different angles:

- The most accurate one is an Excel matrix where actual (=unevenly spaced) observation intervals are compared to ideal (=evenly spaced) intervals.

- This approach turned out to be too complex for programming into a web application (though my daughter is trying it in Python at the moment) so I switched to using the variation ratio (VR) and forgetting about the time aspect.

- Recently, I started using the index of qualitative variation (IQV) because the VR is all about variation around the mode which is not really relevant to the problem at hand.

So my question is this: does anyone know of a good measure for dispersion that covers both dimensions (time and category)? Wikipedia mentions more than a hundred of them but I wouldn’t know where to start.

Your help is greatly appreciated. I can offer nothing in return except gratitude and hopefully an interesting problem.