Zipf's Law, Hierarchical Structure, and Cards-Shuffling Model for Urban Development

Table 3

The hierarchy of the 452 cities in USA and the related measures (2000).

Class (𝑚)	City number (𝑁𝑚)	Average population size (𝑃𝑚)	Average urban area (𝐴𝑚)
1	1	17799861.000	8683.200
2	2	10048695.500	4908.995
3	4	4561564.500	3923.070
4	8	3335242.625	2828.796
5	16	1690796.250	1493.243
6	32	815564.656	899.782
7	64	354537.344	451.605
8	128	156158.125	217.896
9	(197)	69740.228	103.053

Source: The original data come from the US Census Bureau (2002.08.25), only the 452 US cities with population size more than 50,000 are available at the website: http://www.demographia.com/.
Notes: (1) The last class of each hierarchy is a lame-duck class. (2) The unit of population is “person”, and that of urbanized area is “square kilometers.”