# Misleading Graphs

Figure 1, which appeared in Erickson Times, shows the number of Olympic medals won by country. For Germany, the picture of two medals corresponds to almost 500 medals. Therefore, we would expect the picture of four medals to correspond to almost 1000 medals and the picture of six medals to correspond to almost 1500 medals. However, the label for the four-medal picture is 615 and for the 6 medal picture is 1975. Although there is the correct rank ordering, there is little relationship between the pictures of the medals and the labels of the number of medals. Misleading Graphs and Statistics

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It is a well known fact that statistics can be misleading. They are often used to prove a point, and can easily be twisted in favour of that point! The purpose of this section is to learn how to recognize common statisitcal deception so that to avoid being mislead. Bad Sampling When you use a sample to represent a larger group, you must make sure that the people in the sample are fairly representative of the larger group. Example 31. 1 Decide whether a mall is a good place to find a sample for a survey about the amount of allowance received by people ages 10 to 15. Solution.

The mall is probably not a representative place to find a fair sample of people in this age range. Taking a sample at the mall might not represent fairly those people who receive a small allowance, or none Misleading Graphs Good graphs are extremely powerful tools for displaying large quantities of complex data; they help turn the realms of information available today into knowledge. But, unfortunately, some graphs deceive or mislead. This may happen because the designer chooses to give readers the impression of better performance or results than is actually the situation.

In other cases, the person who prepares the graph may want to be accurate and honest, but may mislead the reader by a poor choice of a graph form or poor graph construction. The following things are important to consider when looking at a graph: 1. Title 2. Labels on both axes of a line or bar chart and on all sections of a pie chart 3. Source of the data 4. Key to a pictograph 5. Uniform size of a symbol in a pictograph 6. Scale: Does it start with zero? If not, is there a break shown 7. Scale: Are the numbers equally spaced? 1 The data on the right suggests that the AR program appears to be helping the students.

To make a fair graph of this data, what type of graph would be best? ————————————————- Incorrect origin of the Y-axis JUST LOOK AT THAT UPWARD SPIKE! Oh, the bottom line of the graph isn’t 0, it’s 19 million. The number didn’t triple, despite the looks of things. The most commonly seen “sensationalization” of graphs in the popular media is probably when the graph is drawn with the vertical axis starting not at 0, but somewhere just below the low point in the data being graphed. Both upward and downward trends are exaggerated, for a more exciting look.

For example, the employment data graph to the right, taken from the New Deal article in June 2008, purports to illustrate the level of employment in the United States of America over the years. The amount of employment visually appears to triple from 1933 to 1941. However, the vertical axis begins at 19 million rather than at 0; this disguises the fact that the rise was actually about 56%. For this reason, the graph to the right is misleading. It is certainly more exciting than the “flatter” equivalent, but to be accurate, the graph should have been created with the vertical axis starting at 0.

However, one should also avoid insisting on a misleading “0”. For example, when plotting the temperature history of Boston, it makes no sense to start the plot at 0 K, since 0 K is far removed from physically obtainable values and will only obscure the actual range of variation. In general, if one needs to use an offset 0, it is advantageous to use labels that are large enough that the offset is legible in the thumbnail. ————————————————- Abuse of the X-axis The rightmost of these two graphs was snipped from the “trough” of the leftmost graph.

It would be misleading to use the rightmost snippet to claim to represent data during this time period. Manipulation of the graph’s X-axis can also mislead; see the graph to the right. Both graphs are technically accurate depictions of the data they depict, and do use 0 as the base value of the Y-axis; but the rightmost graph only shows the “trough”; so it would be misleading to claim it depicts typical data over that time period. The graph might not be misleading if it were specifically labeled in the caption as showing data only from 1/10/2008 to 1/13/2008 — but it’s a judgment call whether the wider view would be better anyway.