I have data from 1980 2000, and 2010 from census bureau by block groups and i have geocoded 100 addresses. I am trying to extract data from a buffer zone of 0.5 miles radius around each point. There are about 100 points in different parts of the country.

1. How does one calculate the average of the median income or median housing value within o.5 miles radius of a point/address that might cover as many as four block groups.

We have explored using the average weighted join but found that mathematically its not very solid approach. someone suggested using centroid to calculate the averages but i am clueless as to which tool would work best

1. How does one calculate the average of the median income or median housing value within o.5 miles radius of a point/address that might cover as many as four block groups.

We have explored using the average weighted join but found that mathematically its not very solid approach. someone suggested using centroid to calculate the averages but i am clueless as to which tool would work best

You could use Intersect of your Buffers against the block groups. This should retain the total area of the original census block in the area field, which would be important. If your buffers overlap each other then you will need to Dissolve the Intersected Output using every field as a unique case value except the ObjectID to make sure no Block group is divided into two or more pieces. If you want a weighted average of your block groups you would need to create some fields to multiply the statistics you are after times the portion of area within each block group intersected if it represents a census block average. If the original statistic of the block group represented a census block total or sum, then that values should be mulitplied by the area of the portion that was intersected from the Census Block and then divided by the total Census block area captured by the Intersect. Then Dissolve a second time using just the Buffer IDs as the unique case and summing all of the other statistics (both the original statistics from the blocks for a standard mean and the weighted statistics for a weighted mean). Include a summary statistic that generates a count also just in case, although Dissolve may generate its own count value.

Now if the statistics originally represented an average, maximum or minimum, divide the summaries by just the Dissolve Count and if the statistics were originally an average, minimum or maximum that was weighted by area, divide the summaries by the total area of the newly dissolved buffer. If the summary values were originally a total or sum of the Census Block just divide by the Dissolve Count if they were not weighted and do no division if they were weighted by area. Bottom line is that original census block averages, minimums and maximums have to be handled differently from original census block sums or totals (whether I have worked through the math correctly in the steps I have described or not).

Getting a median or weighted median is trickier. And frankly I would prefer you examine the results of the mean and weighted mean first before going over those methods. The median or middle value will probably be less reliable if the areas covered by the buffer are not all nearly equal or if one area dominates over all of the others (in which case the max area statistics are better). Either way Median will be simply choosing one or the average of two of the census blocks for statistics and ignoring all the other census blocks.

All of the above operate in the absence of any other information about the census block. If you had aerials, parcel valuation data, or land use data, adjustments could be made to account for absences of population or jobs in open space areas, higher or lower valuations of properties and structures, vacant lands, commercial/industrial uses and residential density distributions, etc. If those sources are available they should be sampled to determine how well you analysis correlates with expected results from these sources.