Could somebody please explain this to me. It seems to me that the number of story points actually delivered at the 50th percentile would be more valuable than a theoretical number that is far more likely to get affected by outliers, especially in the early days of an organization adopting scrum.
If you want a statistically significant method to calculate velocity, you might try using the average and standard deviation. This way, you will be able to predict with whichever degree of certainty you are required what your velocity is.
If you wish, you can limit the data to the last few sprints, if you notice a change in the trend, and can explain it as valid.
This goes towards the Agile values of communication and courage (for the stakeholders to accept the uncertainty of the prediction).
e.g.
Team: Based on the last 5 sprints, we are 90% certain that we will be able to deliver at least 30 SP in the next sprint.