Calculating Median of Different Data Groups? Bear with me here. I'm a newbie at this. Let's say we have this data :
+----------+------------+---------+---------+-----+
| regions  | # of orgs  | metric1 | metric2 | ... |
+----------+------------+---------+---------+-----+
| region 1 |        220 |    9800 | ...     | ... |
| region 2 |         18 |    1000 | ...     | ... |
| region 3 |        190 |    5400 | ...     | ... |
| region 4 |         33 |     900 | ...     | ... |
| ...      |            |         |         |     |
| region x |            |         |         |     |
+----------+------------+---------+---------+-----+

For example, in geographical region #1, we have 220 organization where their median number of customer (i.e. metric1) is 9800. 
Now, we have 13 geographical regions that we are interested in, and we want to show metric1 (the median) for each group. Also, we want to show the median for ALL the regions.
My question is: How to calculate the median for all organizations in all regions? Two answers came to us:


*

*Combine all data (# of customers) from all organizations, and we calculate the median like we did for each region. There is one problem, the size of the regions is not the same, which made us think that the result will be biased towards the large regions (region 1 & 3).

*Calculate the median for each region, then calculate the median of the regions' median values. This will remove the bias (we think) but we are not sure if this a valid thing to do , statistically speaking.


Could you please advise us on the correct way to calculate the median without introducing bias?
 A: "The median over all organizations" would be the first thing.
Consider a thought experiment with only two regions. One region has a single organization, and the other all the organizations except that one; let's say there's ten thousand of them.

Now here the median of region A is 60 and the median of region B is 100. If you think the correct thing to calculate is 80 (which lies at the 2.35 percentile of the complete set of organizations) -- i.e. that the thing you want should really give as much weight to one organization as it does to the other ten thousand (if the organizations in region B are counted once, then the one for the smaller region is effectively counted ten thousand times), then what you seek is something other than "the median over all organizations". 
(One question you might like to consider is what quantity is the second thing you mention an estimate of?)
Note that if you wanted an overall mean (what's the mean over all organizations?) then you'd certainly want to give more weight to larger regions, precisely because they have more organizations. Why would the same consideration not apply to the median?
