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Wed, 23 Jan 2008

Smallest state capitals
I think it was James Kushner who first suggested that I consider the question of which U.S. state capital had the smallest population in relation to its state's largest city. For example, New York City is the largest city in the United States, but the state capital of New York State is Albany, with a population of about 850,000. The population of New York City exceeds that of Albany by a factor of around 20.

At the other end of the scale, of course, we have state capitals like Boston, Denver, Atlanta, and Honolulu that are their state's largest cities. For these states, the population quotient is 1, its theoretical minimum.

Well, James, it only took me thirty years, but here it is.

I tried to resolve the question manually a few weeks ago, by browsing Wikipedia for the populations of likely candidates. Today I took a more methodical approach, downloading the U.S. Census Bureau's July 2006 estimates for populations of metropolitan areas, and writing a couple of little programs to grovel the data.

I had to augment the Census Bureau's data with two items: Annapolis, MD, and Montpelier, VT are not large enough to be included in the metropolitan area data file. I used U.S. Census 2006 estimates for these cities as well.

I discarded one conurbation: the Census Bureau includes a "Metropolitan Division" in New Hampshire that consists of Rockingham and Strafford counties; this was the most populous identified area in New Hampshire. It didn't seem entirely germane to the question, so I took it out. On the other hand, including it doesn't change the results much: its population is 416,000, compared with Manchester-Nashua's 402,000.

The results follow.

State Capital and
its Population
Largest metropolitan area
and its population
Quotient
MD Annapolis 36,408 Baltimore-Towson 2,658,405 73.02
IL Springfield 206,112 Chicago-Naperville-Joliet 9,505,748 46.12
NV Carson City 55,289 Las Vegas-Paradise 1,777,539 32.15
VT Montpelier 7,954 Burlington-South Burlington 206,007 25.90
NY Albany 850,957 New York-Northern New Jersey-Long Island 18,818,536 22.11
MO Jefferson City 144,958 St. Louis 2,796,368 19.29
KY Frankfort 69,068 Louisville-Jefferson County 1,222,216 17.70
FL Tallahassee 336,502 Miami-Fort Lauderdale-Miami Beach 5,463,857 16.24
WA Olympia 234,670 Seattle-Tacoma-Bellevue 3,263,497 13.91
AK Juneau 30,737 Anchorage 359,180 11.69
PA Harrisburg 525,380 Philadelphia-Camden-Wilmington 5,826,742 11.09
SD Pierre 19,761 Sioux Falls 212,911 10.77
MI Lansing 454,044 Detroit-Warren-Livonia 4,468,966 9.84
NJ Trenton 367,605 Edison 2,308,777 6.28
CA Sacramento 2,067,117 Los Angeles-Long Beach-Santa Ana 12,950,129 6.26
NM Santa Fe 142,407 Albuquerque 816,811 5.74
OR Salem 384,600 Portland-Vancouver-Beaverton 2,137,565 5.56
DE Dover 147,601 Wilmington 691,688 4.69
VA Richmond 1,194,008 Washington-Arlington-Alexandria 5,290,400 4.43
ME Augusta 121,068 Portland-South Portland-Biddeford 513,667 4.24
TX Austin 1,513,565 Dallas-Fort Worth-Arlington 6,003,967 3.97
AL Montgomery 361,748 Birmingham-Hoover 1,100,019 3.04
NE Lincoln 283,970 Omaha-Council Bluffs 822,549 2.90
WI Madison 543,022 Milwaukee-Waukesha-West Allis 1,509,981 2.78
NH Concord 148,085 Manchester-Nashua 402,789 2.72
KS Topeka 228,894 Wichita 592,126 2.59
MT Helena 70,558 Billings 148,116 2.10
ND Bismarck 101,138 Fargo 187,001 1.85
NC Raleigh 994,551 Charlotte-Gastonia-Concord 1,583,016 1.59
LA Baton Rouge 766,514 New Orleans-Metairie-Kenner 1,024,678 1.34
OH Columbus 1,725,570 Cleveland-Elyria-Mentor 2,114,155 1.23
AR Little Rock 652,834 Little Rock-North Little Rock 652,834 1.00
AZ Phoenix 4,039,182 Phoenix-Mesa-Scottsdale 4,039,182 1.00
CO Denver 2,408,750 Denver-Aurora 2,408,750 1.00
CT Hartford 1,188,841 Hartford-West Hartford-East Hartford 1,188,841 1.00
GA Atlanta 5,138,223 Atlanta-Sandy Springs-Marietta 5,138,223 1.00
HI Honolulu 909,863 Honolulu 909,863 1.00
IA Des Moines 534,230 Des Moines-West Des Moines 534,230 1.00
ID Boise 567,640 Boise City-Nampa 567,640 1.00
IN Indianapolis 1,666,032 Indianapolis-Carmel 1,666,032 1.00
MA Boston 4,455,217 Boston-Cambridge-Quincy 4,455,217 1.00
MN St. Paul 3,175,041 Minneapolis-St. Paul-Bloomington 3,175,041 1.00
MS Jackson 529,456 Jackson 529,456 1.00
OK Oklahoma City 1,172,339 Oklahoma City 1,172,339 1.00
RI Providence 1,612,989 Providence-New Bedford-Fall River 1,612,989 1.00
SC Columbia 703,771 Columbia 703,771 1.00
TN Nashville 1,455,097 Nashville-Davidson--Murfreesboro 1,455,097 1.00
UT Salt Lake City 1,067,722 Salt Lake City 1,067,722 1.00
WV Charleston 305,526 Charleston 305,526 1.00
WY Cheyenne 85,384 Cheyenne 85,384 1.00
Nineteen of fifty state capitals are their state's largest cities.

Vermont is an interesting outlier here. It makes fourth place not because it has a large city, but because its capital, Montpelier, is so very small. I tried doing some scatter plots, to see if anything else jumped out, but they weren't very illuminating. If anything, the data is suprisingly evenly distributed. Here's an example:

The x-axis is the population of the state capital; the y-axis is the quotient. (Both axes are log scale.) Vermont is the leftmost point, near the top. The large collection of points on the x-axis are of course the nineteen states for which the capital and largest city coincide.

[ Addendum 20080129: Some remarks about the format of the Census Bureau's data file. ]

[ Addendum 20090217: A comparison of the relative sizes of each state's largest and second-largest cities. ]


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