The variety of urban environments practice questions.

The populations of a country's cities, from 20 000 to 20 million, are plotted on a vertical axis on which each equal interval represents a successive power of ten. Which statement about reading this axis is correct?

• A straight line on it shows a constant absolute increase each year
• It can only be used for data sets that include negative values
• A straight line on it shows a constant percentage rate of change
• Equal vertical distances on it represent equal absolute differences in population

Answer: A straight line on it shows a constant percentage rate of change

On a logarithmic axis equal vertical distances represent equal multiplications, so a straight line means a constant proportional growth rate rather than a constant amount added each year. The scale is chosen for a rank-size plot precisely because city sizes span several orders of magnitude and a linear axis would press every small town onto the baseline.

A student calculates Spearman's rank correlation coefficient between distance from the city centre and mean plot size for 12 sample sites and obtains rs = +0.64. The critical value for 12 pairs at the 0.05 significance level is 0.591. Which conclusion is justified?

• The correlation proves that distance from the centre causes plot size to increase
• The correlation is too weak to be reported because it lies below +0.70
• The result cannot be tested because rank correlation needs at least 30 pairs
• The relationship is significant at the 0.05 level

Answer: The relationship is significant at the 0.05 level

rs exceeds the critical value, so the probability that the relationship arose by chance is below 5 %. Significance says nothing about causation, and rank correlation works with as few as ten pairs.

A student plans to measure pedestrian flow along a 4 km transect running from the city centre to the rural-urban fringe, in order to test how flow changes with distance. Which sampling method is most appropriate?

• Stratified sampling, with sites allocated in proportion to land use
• Systematic sampling, with one site every 400 m along the transect
• Random sampling, with sites drawn by lottery from the whole city
• Pragmatic sampling, with sites chosen wherever counting is easiest

Answer: Systematic sampling, with one site every 400 m along the transect

A distance-decay hypothesis needs sites at even intervals so that the independent variable changes in a controlled way. Lottery selection would leave gaps along the transect and pragmatic choice introduces bias into where the counts happen.

Land values in a city fall steeply with distance from the centre, and the tallest buildings occupy the smallest plots at the core. Which principle explains this pattern?

• Bid rent: accessibility is greatest at the centre, so users build upwards on costly land
• Distance decay: fewer people are willing to travel far to reach the centre
• Central place theory: the centre has the largest threshold population
• Counter-urbanisation: high-income residents have moved beyond the edge

Answer: Bid rent: accessibility is greatest at the centre, so users build upwards on costly land

Bid rent links the price of land to its accessibility and then explains the built form that follows: where land is dearest, the way to afford it is to use less of it per unit of floor space. The other concepts describe movement or service hierarchies rather than land value.

A city of six million people hosts regional headquarters of banks and law firms, a stock exchange and international air links. Which classification is based on these functions?

• A world city, defined by its command functions rather than its size
• A megacity, defined by having more than ten million inhabitants
• A primate city, defined as more than twice the size of the second city
• A million city, defined by exceeding one million inhabitants

Answer: A world city, defined by its command functions rather than its size

World city status describes a position in global networks of finance, corporate control and connectivity, which is why cities well below megacity size can rank highly. The city is also a million city, but that term, like megacity and primate city, is defined by population size alone and says nothing about the functions listed.

A student compares two cities using population density calculated from each city's administrative area, and concludes that the city with the lower figure is the less crowded place to live. Which weakness in the method is most serious?

• The two administrative areas include very different amounts of undeveloped land
• Density should always be expressed in people per hectare rather than per square kilometre
• The comparison needs total population figures rather than any density measure at all
• Density values can only be compared between cities within the same country

Answer: The two administrative areas include very different amounts of undeveloped land

An administrative boundary is drawn politically: one city may be tightly bounded to its built-up edge while the next includes farmland, forest and reservoirs. A density calculated that way describes the boundary as much as the crowding, which is why comparisons use the continuous built-up area instead.