One of the things to take away is that it's often counter-productive to take one summary statistic like "mean" or "median" and try to just optimize that. The correct strategy is likely to be a bit more nuanced and depend on your specific situation.

For example, maybe you have a few different pricing tiers, and instead of optimizing for ARPU, you optimize for the number of people in a given tier that you can up-sell into a higher pricing tier. Now you're optimizing for something meaningful. Note that even if you did a good job in accomplishing this goal, your ARPU might actually go down, if you simultaneously saw a lot of growth in your lower pricing tiers from new signups.