To make graphs look more interesting, many authors have resorted to making pictograms such as the following. This graph charts the number of medals won by country at the Olympics. But instead of using a standard bar graph, the author has replaced the bars with medals to make the graph look better. However, although the countries are correctly ranked in order, the medal icons aren’t proportional to the numbers they represent. The two medal icons for Germany, for instance, represent 499, but the four medal icons for Britain represent 615. This is misleading because 615 is not twice of 499.

Source: Omaha World Herald

As another example, consider the graph to the left which compares the proportion of Nebraskans in jail, on parole, on probation or in juvenile detention in 1982 and 2007. In this case, thumbprints have been used to represent the numbers. However, like a bar graph, only the height (and not the area) of the thumbprint matters in this graph. Since the number in 2007, 2.27%, is almost double the number in 1982, 1.15%, the height of the thumbprint on the right has been made to be twice the height of the thumbprint on the left. But the width of the thumbprint on the right has also been made twice that of the thumbprint on the left. The area of the figure on the right is therefore four times the area of the figure on the left. So if someone were to look only at the area of the thumbprints, they would mistakenly think that the proportion of Nebraskans under correctional control in 2007 was four times the proportion in 1982.

While the size of the “bars” in the previous graphs were not proportional to the numbers they represented, there was at least a bit of a relationship between the size of the bars and the data, in that the larger the number was, the larger/longer was the “bar”. But some graphs, such as the following, are so misleading that the lengths of the bars have no relation whatsoever to the data. In other words, the bars are totally irrelevant. If you looked only at the lengths of the bars, you’d think that New York had more high school athletes than did California, but the numbers tell a different story. In reality, this “graph” is just a table with some fancy formatting.

Discussion

Source: http://jacklucky.posterous.com/top-20-countries-generating-visitors-to-the-u

The figure above shows the number of tourists from each country to the US for the top 20 countries.

Do the lengths of the sections for each country correspond to the numbers they represent? If not, what do you think the lengths of the sections correspond to, if anything?
Are the positions of the sections in any particular order?
Do you think there has been any benefit to making the graph this particular way (i.e. in the form of a snake)?
What changes would you make to the graph to make it more informative?

Outcomes

12C.D.2.3

Interpret statistics presented in the media, and explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view

12C.D.2.4

Assess the validity of conclusions presented in the media by examining sources of data, including Internet sources (i.e., to determine whether they are authoritative, reliable, unbiased, and current), methods of data collection, and possible sources of bias (e.g., sampling bias, non-response bias, a bias in a survey question), and by questioning the analysis of the data (e.g., whether there is any indication of the sample size in the analysis) and conclusions drawn from the data (e.g., whether any assumptions are made about cause and effect)

Misleading Pictograms (Investigation)