Determining the Median of Five Median Numbers

[Patty Kirk]

Problem:
My goal is to show the median income among five different groups of people, where the median income for each group has already been determined. Is it as simple as choosing the median income of $ 45,615 since there are five numbers? Here is the information:

Group One's Median Income $35,628
Group Two's Median Income $44,320
Group Three's Median Income $45,615
Group Four's Median Income $49,942
Group Five's Median Income $57,021

Thank you very much; I hope I have followed the proper procedure in submitting this request as this is my first one.

 

[haruspex]

There is no way to do that except in the special case where the individual groups all have the same median Too much information has been lost.
Even if all the groups are the same size you cannot do it. E.g. consider the two groups
19,19,19,21,99,100, median 20
17,18,19,21,22,23, median 20
If we bring in a third group of six with median 30, say, the overall median will depend on how many in it are below 20.