I was thinking about this, and came to realize that even though the sky-high values appear to be anomalies, in reality, they were not binary events. That is, given that those high values happened, and that they progressively decreased towards the normal-times lower values with each successive cycle, it would make sense to actually leave them in the mean table. That would seem to provide a more relevant mean trend.
As for the median chart, I agreee that it gets skewed by those cycles. However, rather than remove them from consideration, there should be some mathemagical method to integrate that information.