IB Geography
The Lorenz Curve is a graphical method used to display the concentration of activities within an area (e.g. the degree of industrial specialization within an urban area). Fieldwork data may be used but it is more common to use secondary sources (e.g. census data, etc). This technique is particularly useful as it provides a good visual comparison of any observed differences and from it a precise index (Gini Coefficient) can be calculated.

The further away the Lorenz Curve is from the "line of perfect equality" (diagonal), the more diverse is the sample and the more unevenly the values are spread out . This is very useful to estimate how wealth is distributed among a population: if a country's Lorenz Curve is distant from the line of perfect equality, it means a small % of the population controls most of the wealth and that the country's income distribution is uneven.

Picture
In a perfectly equal country, 60% of the population should earn 60% of the country's wealth, but in this example:
  • 60% of the population of country X earns 20% of the country's wealth
  • 60% of the popuation of country Y earns 15 of the country's wealth
This means that the income distribution in country Y is more unequal than in country X
To draw a Lorenz Curve, follow these steps:
  1. Gather the data (e.g. census data from two cities)
  2. For each set of data, rank the categories and order them by rank in a table
  3. Convert each value in a % of the total
  4. Calculate the running totals (ie cumulative %, by adding the % of one line to the ones before)
  5. Graph ranks (horizontal) against cumulative % (vertical)
  6. Draw the "even distribution line" running from (rank = 0, % = 0) to (rank = max, % = 100%), which represents the line if all the categories were the same size.
Example: comparison of employement between city block #1 and city block #2
Employment survey in city block #1:
Occupation
Number
employed
Rank
Frequency
(= % of total)
Cumulative
Frequency %
Office workers
195
1
60%
60%
Retail workers
34
2
10.5%
70.5%
Waiters
25
3
7.6%
78.1%
Teachers
23
4
7.1%
85.2%
Public Employees
28
5
5.5%
90.7%
Managers
16
6
4.8%
95.5%
Doctors
7
7
2.1%
97.6%
Unemployed
6
8
1.8%
99.4%
CEOs
1
9
0.6%
100%
Employment survey in city block #2:
Occupation
Number
employed
Rank
Frequency
(= % of total)
Cumulative
Frequency %
Waiters
19
1
26.3
26.3
Managers
18
2
25%
51.3%
Office workers
14
3
19.4%
70.7%
CEOs
6
4
8.3%
79.0%
Doctors
5
5
6.9%
85.9%
Retail workers
5
6
5.5%
91.4%
Public employees
3
7
4.2%
95.6%
Unemployed
2
8
2.9%
98.5%
Teachers
1
9
1.5%
100%

Picture
Graphic interpretation:The Lorenz Curve for the city block #2 (red) is closer to the Even Distribution Line (blue) than for city block #1 (green): this means that various types of jobs are more evenly distributed in city block #2, while more people tend to do the same kind of work in city block #1 (e.g. 60% of them hold the type of work found at rank #1, ie office workers).

However, in both cases, we find that there appears to be a significant deviation from the "ideal" line of even distribution, which means that in both cases, there isn't much diversity in the types of jobs found in both blocks: just two types of jobs employ 50% (city block #2) to 70% (city block #1) of all people, while other types of jobs are much less represented.