It is often said that a “picture is worth a thousand words.” And graphs, just like other types of pictures, can provide a wealth of information to the viewer in a highly succinct manner. However, this information, just like other pictures, can be biased, misleading or just plain wrong.
People often assume that graphs published in newspapers or used in advertisement must be based on factual information and therefore, provide an accurate representation of the data. Students, who are new to graphing and have just mastered the skills required to create bar, line and circle graphs, are even more likely to accept graphical representation of data as fact. Although standard middle school curricula often provide a unit on misleading graphs, little time is actually spent analyzing the data behind the graph and how it was collected. Nor is much time spent focusing on the potential bias of the author and how this bias may affect the graphical presentation.
Students also have a poor understanding of measures of central tendency, often assuming that the arithmetic average, or mean, is the only true measure and should therefore be accepted as the best representation for the data. (This belief is shared by many adults as well.) Students need experiences working with data sets that have a normal distribution, bi-modal distribution or skewed distribution to see how this may affect their choice for the best “average.” By analyzing the underlying data in greater depth, students will gain more insight into the meaning behind these statistics. It is hoped that students will learn to question statements which claim characteristics of the “average” person or the “average” income.
In this curriculum unit, students will be introduced to different methods of manipulating data and graphical presentations to prove a point or mislead the viewer. Students will learn to analyze existing graphs to determine whether or not they show a bias. They will learn to question data collection methods and the calculations behind various “averages.” They will identify the various graphical techniques often used to prove a point, deceive the viewer or to exaggerate a position. Finally, students will be asked to create a series of their own graphs to argue opposing sides of a single position.