I am trying to calculate the "overall" median of a variable that is spread across two datasets. I have access to the raw data in each dataset but can't bring their raw data together. What would be the best way to calculate the median (or any quantile for that matter)? What I was thinking to do was to get the quantiles from the "remote" dataset, say with N_1 samples and bring them to the other dataset; then sample N_1 values from these quantiles (essentially discrete empirical CDF) and use these values as "raw" scores to calculate the overall median or any other quantile. I wonder if there is a more sophisticate way of doing this?

I can't combine the two datasets because of data governance issues, where I have to analyse them separately on different computers.