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The Rank-Size Rule
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The lesson provides an explanation of the Rank Size Rule of Zipf.

Maitrayee Mullick
I hold a Master's degree in Geography and also have qualified for the UGC NET (JRF). Recipient of the Jony Ive Award from Unacademy.

U
sir we r very very thankful to you for this and plz continue this .
Mukesh Agrawal
a year ago
I have again started do check out.
thank you so much ma'am for this awesome lesson :)
You're most welcome. :)
1. The Rank-Size Rule presented by Maitrayee Mullick https://unacademy.com/user/maitrayee2295

2. The Rank-Size Rule presented by Maitrayee Mullick https://unacademy.com/user/maitrayee2295

3. The Rank-Size Rule presented by Maitrayee Mullick https://unacademy.com/user/maitrayee2295

5. Topics to cover in the lesson.... Zipfs Law and the Rank-size Rule Pattern as per rank- size rule Known exceptions to simple rank-size distributions What is the Rank- size rule

6. The concept of Rank-Size Rule or Rank-Size Distribution Cumulative frequency is defined as the running total of frequencies. It is the sum of all the previous frequencies up to the current point The Rank-Size Rule was revealed in both developed and underdeveloped countries when the cumulative frequency of cities with a population of greater than twenty thousand people was ranked against the size of a city on a log-normal scale A logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include earthquake strength, sound loudness It is based on orders of magnitude, rather than a standard linear scale, so the value represented by each equidistant mark on the scale is the value at the previous mark multiplied by a constant. Rank Size Rule is a simple model which states that population size of a given city tends to be equal to the population of the largest city divided by the rank of the given city. 8

7. Any criteria for optimum population size involve:s implicitly and explicitly two elements: 103 102 10 log1o(F (x))-2log10(x)+4 first the normative element, which places a positive or negative valuation in a particular situation and second a factual element which has the force of the statement of empirical relationships between variation in city size and variation in situation question. 100 101 102 10 1030 9

8. Rank-Size Rule And Developing Countries The most complete and comprehensive empirical study of the rank-size rule in developed and developing countries is that by Berry who analyzed city size distributions and their relationship to economic development in thirty-eight countries. He found that the distributions fall into two major categories namely the Rank Size Distribution and the Primate Distribution 10

9. 'In an ordered set of cities representing a given country, the product of the rank and size of a city is constant' (Dziewonski 1972: 73) 12

10. The relationship between size and rank of citie:s Zipf's has probably the best presentation of the empirical findings on rank and size of the cities. The rank size rule states that for a group of cities, usually those exceeding some size in a particular country, the relationship between size and rank of cities is given by: Pr P1/r Where Pr population of the largest city ranked r P population of the largest city r rank of city r Rank Size Rule is a simple model which states that population size of a given city tends to be equal to the population of the largest city divided by the rank of the given city. 14

11. 1000 Towns plotted according to their population size THE RANK-SIZE RULE: GRAPHICAL REPRESENTATION 100- 10- 100 1000 15 Rank Size (in log scale)

12. Pattern as per rank-size rule Settlements in a country may be ranked in order of their size. The 'rule' states that, if the population of a town is multiplied by its rank, the sum will equal the population of the highest ranked city It is usually possible to relate the ranks and sizes of the central places in country by using a regression analysis log Pk log P, b log k In other words, the population of a town ranked n will be 1/nth of the size of the largest city-the fifth town, by rank, will have a population one- fifth of the first 16

13. Pattern as per rank-size rule log Pk log P,-b log k The greater the value of b, the steeper the slope, and the greater the primacy of the largest city or town. Many developing countries show a sharp fall from the largest, primate city to the other cities, o where P, is the population of the largest city or town, Pk is the population of the kth town by rank, and b is a coefficient which must be established empirically for each investigation d this is known as the primate rule. 17

14. Pattern as per rank-size rule 1000 The theoretical rank size rule pattern is a straight line. In urban primacy, a single city dominates and is much greater than the next large center (primary pattern). Towns plotted according to their population size 100 In Binary pattern two or more cities are In Stepped order pattern there are series larger than the predicted size. 10 of levels and steps (conurbations, cities, towns etc.). 10 100 18 Rank Size (in log scale)

15. Known exceptions to simple rank-size distributions While Zipfs law works well in many cases, it tends to not fit the largest cities in many countries; one type of deviation is known as the King effect. A 2002 study found that Zipfs law was rejected for 53 of 73 countries, far more than would be expected based on random chance A 2004 study showed that Zipfs law did not work well for the five largest cities in six countries. The United States, although its largest city, New York City, has more than twice the population of second-place Los Angeles, the two cities' metropolitan areas (also the two largest in the country) are much closer in population. In metropolitan-area population, New York City is only 1.3 times larger than Los Angeles. In other countries, the largest city would dominate much more than expected. For instance, in the Democratic Republic of the Congo, the capital, Kinshasa, is more than eight times larger than the second-largest city, Lubumbashi. 19

16. That's all for now...stay tuned for more... Maitrayee Mullick Follow for upload notifications 3171 All counses 20