I do a bunch of Real Estate Reporting and the Median price is often reported. Particularly by the NAR (National Association Of Realtors) ,,, How can this be,, As best I can figure they only get the Medians from each area,, so how should they calculate a national median, a median of medians a a simple average of medians or weighted average of medians or....??? How valid can it be,, I know that the NAR is not getting the total transaction table so can a reasonable representation of Median (nationally be done? Particularly since regional density and prices and market variances are so large now?
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.