Visualizing statistics with maps

Information graphics, and the data visualization techniques that support their use – plots, charts, graphs, maps – have become important tools in disseminating information. A well-designed graphic, devised to clarify or confuse, depending on the designers motive, holds the power to influence decisions we make every day about the food we eat, the products we buy, the services we use, and even who we elect to office.

In ‘How to Lie with Statistics‘, an excellent introduction to the use and abuse of statistics, Darrel Huff describes one such visualization tool, the map, as follows:

One of the trickiest ways to misrepresent statistical data is by means of a map. A map introduces fine bag of variables in which facts can be concealed and relationships distorted. My favorite in this field is “The Darkening Shadow.” [1]

The map shows what portion of our [US] national income is now being taken, and spent, by the federal government. It does this by shading the areas of the states west of the Mississippi (excepting only Louisiana, Arkansas, and part of Missouri) to indicate that federal spending has become equal to the total incomes of the people of those states.

The deception lies in choosing states that have large areas, but because of sparse population, relatively small incomes. With equal honesty (and equal dishonesty) the map maker might  have started shading in New York or New England and come out with a vastly smaller and less impressive shadow. Using the same data he could have produced quite a different impression in the mind of anyone who looked at this map.

“The Darkening Shadow”, Graphic Presentation by Brinton, Willard Cope

Much of the subterfuge described above, relies on understanding the frailties of the human brain. The human brain interprets visual information faster than information presented with language or numbers. The brain is also incredibly lazy, predominantly running on autopilot, invoking its critical faculties only when faced with unfamiliar situations or confusing information. If the brain perceives a piece of information as familiar, it quickly falls back to its uncritical default mode: the chief reason for most mistakes we make.

Here’s another example from more recent history. A couple of days after Donald Trump won the electoral college vote in the 2016 US presidential election, several messages were circulated on various social media channels[2] with a statistically dubious claim that 90% of the US voted for Trump. All the polls leading up to the election had predicted a tight race (although they also predicted Hillary Clinton would win). Importantly, though, when this image was being circulated Clinton was leading the popular vote.[3]


So how can someone that only 10% of the country endorsed lead the aggregate vote count? The image above, intentionally or otherwise, relies on the same kind of deception described in Brinton’s “The Darkening Shadow” example. A quick glance at the map shows that vast areas of the US did vote for Mr.Trump. However, it conceals (or does not reveal) a critical piece of information required to make sense of this map: the population density of the various states.[4]

US States population density (persons per square mile) [4]

Population density varies widely across the United States, from approximately  1 person/square mile in Alaska to a little over 780 persons/square mile in Massachusetts. A choropleth map, one that took population density into account – where areas are shaded in proportion to a variable – would have presented a more realistic picture of the race. A seemingly unimportant detail was sufficient to misguide our judgment.

Want to know more about how we can be deceived by statistical data?  Pick up a copy of How to lie with Statistics, one of six books in recommended by Bill Gates’ reading list for 2015.

References and Footnotes

[1] “The Darkening Shadow” on

[2] The influence of social media should not be overlooked; many people consider it their primary source of news.

[3] Clinton eventually won the popular vote about 3 million votes ahead of Trump. Detailed spreadsheet from cookpolitical with vote breakdown by state.

[4] District of Columbia excluded from the image; the abnormally high population density skews the rest of the chart. An interactive version of the population density chart can be found here.

[5]  Data from US Census Bureau: population numbers, areas of states.