Consistent Education Divide in Cities

The Daily Viz brought this to my attention. It's a visual by the New York Times showing how the distribution of cities by proportion of adults with college degrees has changed over the last 40 years.

Nicely formatted and presented, though my ability to compare the distributions side-by-side is a little bit limited.

The key story that this visual is telling is that the average has moved from 12% to 32%, but that the number of cities more than 5% above or below the average has increased substantially. "College graduates are more unevenly distributed in the top 100 metropolitan areas now than they were four decades ago." But i'm not sure if it's as simple as that.

Suppose I was measuring trees. One species was 10 feet tall on average and species two was 100 feet tall. If the first tended to vary between 7 feet and 13 feet, but the latter tended to vary from 85 feet to 115 feet, I wouldn't remark at how much more variable these trees were. For species one, no tree was more than 3 feet from the average, but in species two, presumably many are. Is this a sign that species two is more unevenly distributed? Not really. Species one varies up and down by 30% where two does so by 15%.

So I asked myself, given that the average proportion of adults with college degrees has nearly tripled to 32%, has their variability increased proportionally? Now that these trees are 32 feet tall, it seems strange to still measure their "unevenness" by how many of them are between 27 and 37.

So I reached out to a statistic, the Coefficient of Variation. Using my eyes to collect the data from the charts (so not precisely the correct data), I calculate a coefficient of 0.25 in 1970 and 0.22 in 2010. The variation in the data as a proportion of the average has gone down in the last four decades.

Again, the NYT concludes that "College graduates are more unevenly distributed in the top 100 metropolitan areas now than they were four decades ago.", but I would argue that if anything they are slightly more evenly spread than before and not remarkably so.