I do a bunch of real estate reporting and the median price is often reported, particularly by the NAR (National Association Of Realtors). As best I can tell, they only get the medians of real estate prices from each area. My question is, how should the national median be calculated, given the data restrictions? As a median of medians, as a simple average of medians, or weighted average of medians or something entirely different? Second, how valid would these estimates be? I know that the NAR is not getting the total transaction table, so can a reasonably accurate representation of the median still be estimated at the national level? I ask, in particular, because regional density and prices and market variances are so large.

  • 6
    $\begingroup$ Can you please work on the style and clarity of your question? $\endgroup$
    – user88
    Commented Nov 11, 2010 at 23:13
  • 4
    $\begingroup$ if I understand this correctly, dartdog wants to know whether the median of medians is the can be used to calculate the median of the whole sample, i.e. if $M=M_1 \cup M_2 \cup \ldots \cup M_k$ then median($M$)=median(median$(M_1)$,median$(M_2)$,$\ldots$,median$(M_k)$)... $\endgroup$
    – psj
    Commented Nov 13, 2010 at 19:23

1 Answer 1


The median of medians is not the same as the median of the raw scores. A simple case of this is that when you have an odd number of sales, the median is the middle value; when you have an even number of sales, the median is commonly taken as the average between those two values. A more "real world" challenge to this is that states will sell differing numbers of houses and thus the median of their medians is a poor guess as to the median of all home sales. Though it also will to be precise, a good first pass estimation would be to find the median of values where each state's median is reflected a number of times proportional to the number of sales in that state. Thus, I am essentially suggesting a weighted median.

  • $\begingroup$ drknexus You get the issue I was driving at,. The issue is that the national housing stats often report national medial house prices,, but I'm pretty sure they at best get the median values for a state so I believe that the "national" median house price statistic is pretty bogus. Particularly when one realizes that the mix of demand by state probably fluctuates quite a bit as well due to local economic conditions and local foreclosure trends (which vary widely). So, Is there a semi valid way to do this is is it as bogus as I suspect?? $\endgroup$
    – dartdog
    Commented Jan 19, 2011 at 22:33
  • 1
    $\begingroup$ <shrug> It is 'valid' to whatever extent it represents the information you are interested in/the extent to which it represents what it purports to represent. If the people doing these analyses have the raw data that allows them to find the median by state, I see no compelling reason they would opt to report the median of state medians rather than just the overall median, because (as you suggest) the overall median has a clear interpretation whereas the median of medians does not. $\endgroup$ Commented Jan 20, 2011 at 0:57
  • 1
    $\begingroup$ P.S. You can spot check their technique if you can find the median by state. If their reported median national house selling price matches the median of reported state medians - then they are doing what you fear. If not, then you can probably assume that they are using the simple median of all houses sold. $\endgroup$ Commented Jan 20, 2011 at 0:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.