Symmetric vs Non symmetric

Extreem and influential observations

Mean is heavily affected by influential observations.
Median is more robust.

Cumulative Distribution

Show all the data points at once with their contribution to the distribution of the value x
See Ch. 8 Visualizing distributions: Empirical cumulative distribution functions and q-q plots in Fundamentals of Data Visualization (Wilke 2019)

From a density to a cumulative distribution

How to:

Order all observation ascendingly.
Plot cumulative frequency for every existing observation on Y axis.

Cumulative distribution of income (1)

Cumulative Distribution: applications

Measuring income inequality

Income inequality

Lorenz curve

The Lorenz curve:

Is a cumulative distribution
Arrange all individuals by increasing income
- from 0% to 100% of maximum income.
Compute cumulative % of people by income level (0 to 100% of all people).
see Graphical representation of the Lorenz curve.

Lorenz curve: spot any differences

Example: Lorenz curve

How has income distribution changed between 1988 and 2011?
What statistical concept underlies the computation of the Lorenz curve?
See also: https://ourworldindata.org/the-history-of-global-economic-inequality

Homework examples

Lorenz curve

Draw two Lorenz curves both with unequal income distribution.
Explain differences between two curves?

At home: Read what is the Gini Coefficeint

Joe Hasell (2023) - “Measuring inequality: What is the Gini coefficient?” Published online at OurWorldInData.org. Retrieved from: https://ourworldindata.org/what-is-the-gini-coefficient [Online Resource]

At home: Lorenz curve: Inequality

What kind of plot is this?
What does it show?
Which of these two countries demonstrate more equal distribution?
Why do you conclude this?

Todaro, Michael, and Stephen C. Smith. 2014. Economic Development. 11th ed. Pearson.

Wilke, Claus O. 2019. Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures. O’Reilly Media.