First of all, most of the data that is widely used on this comes from the Bureau of Labor Statistics. They report the unemployment rate, labor force, and employment totals for each month for a wide variety of places around the country, as well as state and city totals. I'll break it down a bit more and then the problem should be clear.For any Metropolitan Area -- think D.C./Arlington/Alexandria/etc altogether--the Bureau of Labor Statistics (BLS) reports an unemployment rate. For the Washington Metro Area, this was 6.1% in January -- the lowest in the nation at the time. Of course, there's a high degree of variance among the different cities in the metro area. The city itself of Washington D.C. had an unemployment rate that month of 10.1%. Arlington County was at 4.1%, and Alexandria City was at 4.9%. So if you just looked at the metro area as a whole, you'd be missing out on all of that variation, and you'd be claiming something -- DC has a great economy -- that just isn't true for the city itself.But you can clearly go further than that: the wards don't all have the exact same economic conditions, and the unemployment rate is lower in some and higher in others. The highest at the time was Ward 8 at 25.2%, while Ward 7 was a good chunk lower at 17.1%. Ward 3 had the lowest, at a mere 2.7%. There is clearly a huge amount of variance just within the city.
Now, here is where we run into problems. The BLS releases data for states, metropolitan areas, counties, and cities with a population larger than 25,000--for privacy purposes, they don't do anything smaller. Some state-specific agencies (like the California website I linked to below, http://www.labormarketinfo.edd... ) release the data for smaller cities and towns too, with some of the numbers fuzzed a bit. But nobody (that I've been made aware of) broadly releases the data for sub-city areas like the wards. This means that when making the comparison in the linked piece, they were comparing the worst rate for any of the wards of DC with the average rate of other cities.As a particular example, Detroit had an unemployment rate in January of 20%. That's the average for the whole city--so it's worse in some parts and better in others. I don't know Detroit that well, but it seems likely that if you divided it up and looked at some of the poorer pieces, the unemployment rate would be much higher than even in Ward 8. Without that kind of data for Detroit (and New York, and LA, and etc etc etc), knowing the breakdown of the different areas in DC just doesn't tell us anything about how DC is relative to other cities.To go even farther, the city of Delano, CA (population 53,041) had an unemployment rate of 39.6% in January. Ward 8 has a population of around 73,000. So unless the Bloomberg writers were being very very particular when they said "comparable size", they weren't even correct that Ward 8 had the highest, so they were wrong on their own terms.But in the end, I don't think this does much to change your concluding point. The black population in DC covers a huge swath of economic life, from the 25% unemployed in almost entirely black Ward 8 to the President sitting in the oval office. The demographic profile of the white population, on the other hand, is much more skewed, and reflects--as you said--the substantial educational, social, and other differences between the median white person in DC and the median white person elsewhere.
Journalists aren't known for judicious use of statistics. Fortunately, I have the Horde.