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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.

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    $\begingroup$ Can you please work on the style and clarity of your question? $\endgroup$ – user88 Nov 11 '10 at 23:13
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    $\begingroup$ 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 Nov 13 '10 at 19:23
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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.

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  • $\begingroup$ 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 Jan 19 '11 at 22:33
  • $\begingroup$ <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. $\endgroup$ – russellpierce Jan 20 '11 at 0:57
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    $\begingroup$ 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. $\endgroup$ – russellpierce Jan 20 '11 at 0:59

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